The Arabic word for orphan is yatîm(يتيم). Any child (male or female) whose has no father or whose father has died and the child has not reached the age of Puberty (+/- 14 years) will be classified as a yateem or an orphan in Islamic Jurisprudence.
Its linguistic meaning is simply "something that is singular and alone." When the word is used in the context of a human being, it means "a minor who has lost his or her father."
Generally, an orphaned child is confronted by poverty and has a weak position in society. A minor child in such a compromised set of circumstances possesses nothing, not even the knowledge of how to cope. A child does not have the experience and life skills to make it on his or her own.
Alî b. Abî Tâlib (R) relates that the Prophet (ﷺ) said: "There is no orphan beyond the time of puberty, and there is no observing a day of devotional silence (in Islam)." Sunan Abî Dâwûd (2489) and authenticated by Al-Albânî
However, the term "orphan" can apply figuratively to an adult, by way or referring to a person with reference to what that person used to be.
1. And do not approach the orphan's property except in a way that is best until he reaches maturity. And give full measure and weight in justice. We do not charge any soul except [with that within] its capacity. And when you testify, be just, even if [it concerns] a near relative. And the covenant of Allah fulfill. This has He instructed you that you may remember. Surah Al An’am 6:152
2. And do not approach the property of an orphan, except in the way that is best, until he reaches maturity. And fulfill [every] commitment. Indeed, the commitment is ever [that about which one will be] questioned. Surah Al Isra 17:34
3. Allah, in His providence, decreed that the Prophet (peace be upon him) would be sheltered and cared for after losing his parents. Allah says: "Did we not find you an orphan and give you shelter." Sûrah al-Duhâ: 6
4. So as for the orphan, do not oppress [him].Surah Al Duha 93:9 
Another instance we find the word orphan used to refer to someone who has already attained the age of majority is where Allah says: "If you fear that you will not deal justly with the orphans, then marry (other) women of your choice…" Sûrah al-Nisâ': 3
Then there is where Ibn `Abbâs relates that the Prophet (ﷺ) said: "The widow has more rights to decide her affairs, and the orphans consent is to be sought from her, and her silence is her consent." Musnad Ahmad 2247
Prophet (ﷺ) said, holding up his two fingers together: "The one who takes care of an orphan is with me in Paradise like this." Sahîh al-Bukhârî 5546 and Sahîh Muslim 5296 
Sponsoring an orphan is one of the righteous deeds which Islam encourages us to do and tells us are among the means of entering Paradise, and indeed of attaining the highest positions therein. There is sufficient encouragement for the believer to do these actions in the words of the Prophet ﷺ: “I and the one who sponsors an orphan will be in Paradise like these two” – and he gestured with his forefinger and middle finger, holding them apart. Al-Bukhari, 5304.
Spending money on an orphan is something that is encouraged in particular. The Prophet (ﷺ) said: “This money is fresh and sweet. Blessed is the wealth of the Muslim, from which he gives to the poor, the orphan and the wayfarer” or as the Prophet ﷺsaid it. Narrated by al-Bukhari, 1465; Muslim, 1052.
But this spending is not the be-all and end-all of the sponsorship that is encouraged in Islam, for which a person is promised a high status in Paradise, rather it is just one kind and one aspect of sponsorship and kind treatment of the orphan until he grows up.
Rather sponsorship in the complete sense means looking after him, guiding him with regard to his religious and worldly affairs, educating him, and treating him kindly until he is no longer regarded as an orphan (i.e., when he reaches adulthood).
Ibn al-Atheer said: “The sponsor is the one who takes care of the orphan’s affairs and brings him up.” Al-Nihaayah, 4/192.
In Riyaadh al-Saaliheen, al-Nawawi (may Allaah have mercy on him) defined the sponsor of an orphan as being the one who takes care of his affairs. The commentator on this book said: (that means) his religious and worldly affairs, by spending on him, clothing him, etc. Daleel al-Faaliheen, 3/103.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said: Sponsoring an orphan means taking care of his religious and worldly interests, teaching him and guiding him etc with regard to religious matters, and taking care of his food, drink, shelter and other worldly concerns. Sharh Riyaadh al-Saaliheen, 5/113.
The religious and educational affairs of the orphan both come under the heading of sponsorship; it is not only the matter of material, worldly interests. Indeed, these (religious and educational interests) are more important, just as a father’s educating and disciplining his children is more important than his simply spending on them.
Shaykh Ibn Sa’di said – concerning a man educating his children: When you feed them, clothe them and train them physically, you are fulfilling their rights for which you will be rewarded; by the same token, when you train them spiritually and impart beneficial knowledge to them, and guide them towards good morals and manners and warn them against the opposite, you are also fulfilling rights which are even more important.” Bahjat Quloob al-Abraar, 128.
This is the true sponsorship of an orphan, bringing him up like one's own son, which is not limited to feeling compassion for him and being kind to him, and teaching him and disciplining him and educating him in the best manner. Fayd al-Qadeer by al-Manaawi, 1/108.
Al-‘Iraaqi (may Allaah have mercy on him) wondered whether this was the reason why the one who sponsors an orphan would be close to the Prophet ﷺin Paradise. He said: “Perhaps the reason why the one who sponsors an orphan will be so close to the Prophet ﷺin Paradise is because a Prophet ﷺis usually sent to people who do not know about Allaah and the true religion, so a Prophet is like a sponsor, teacher and guide for them, and the one who sponsors an orphan is taking care of one who does not understand his religion, or even his worldly affairs, so he guides him, teaches him and disciplines him. Quoted by al-Haafiz in al-Fath, 10/437.
Moreover, limiting it to spending, especially when the orphan is far away, deprives the sponsor of one of the means of softening the heart and meeting needs, which is embracing the orphan and treating him kindly. The Prophet ﷺsaid: “Bring the orphan close to you, wipe his head and give him some of your food, for that will soften your heart and fulfil your need.” Al-Silsilah as-Saheehah, 854.
The point is that the best way of sponsoring an orphan is for a man to bring him in with his own children, and raise him as he raises them, and spend on him as he spends on them.
If the sponsor cannot afford to spend on the orphan, or if the orphan has enough wealth to be independent of means, and a man brings him in with his own children, this is good, even if it is lower in status than the first suggestion. This is one of the greatest types of sponsorship, and serves one of its greatest aims.
Al-Nawawi (may Allaah have mercy on him) said: “This virtue is attained by the one who sponsors an orphan from his own wealth or from the orphan’s wealth under legitimate shar’i guardianship. Quoted by Ibn ‘Alaan in Daleel al-Faaliheen, 3/104.
If a man has wealth from which he can spend on an orphan, as in the case of the person asking this question, then he is doing something very good and it will be sufficient to protect him from the fitnah (trial, temptation) of wealth and stinginess. And it will fulfill the condition stipulated by the Prophet ﷺ: “… from which he gives to the poor, the orphan and the wayfarer.” But this is not sponsorship in the fullest sense, for which a person is promised closeness to the Prophet ﷺin Paradise.
But if he has a pure and sincere intention he may achieve thereby that which he could not attain by his deeds. It was narrated from Anas (R) that the Prophet ﷺwas on a campaign and he said: “There are people whom we have left behind in Madeenah, but we did not travel though any mountain pass or valley but they were with us. They were detained by some excuse.” Sahih al-Bukhari, 2839. 
Allah has allowed sponsoring of an Orphan but has forbid adoption.
Adoption means that a man takes an orphan and makes him like one of his own children, calling him after him, so that the orphan is not allowed to marry one of the man’s daughters, and so the sons of the adoptive father are regarded as brothers of the orphan and his daughters are regarded as his sisters, and his (the father’s) sisters are regarded as his paternal aunts, and so on. This was one of the things that were done during the first Jaahiliyyah, and some of the Sahaabah carried the names of their adoptive fathers, as in the case of al-Miqdaad ibn al-Aswad whose real father’s name was ‘Amr, but he was called ibn (son of) al-Aswad, after the man who had adopted him.
This continued into the early days of Islam, until Allaah forbade that, according to a well-known story. Zayd ibn Haarithah was called Zayd ibn Muhammad, and he was the husband of Zaynab bint Jahsh, then Zayd divorced her.
Allaah has forbidden adoption because it causes knowledge of people’s lineage to be lost, and we have been commanded to preserve people’s lineage.
It was narrated from Abu Dharr (R) that he heard the Prophet ﷺsay: “There is no man who knowingly calls himself after someone other than his father but he has committed kufr. Whoever claims to belong to people to whom he has no ties of blood, let him take his place in Hell.” Narrated by Sahih al-Bukhaari, 3317; Sahih Muslim, 61
The Messenger ﷺsaid that sponsoring orphans is a means of being together with him in Paradise.
It was narrated that Sahl ibn Sa’d said: The Messenger of Allaah ﷺsaid: “I and the one who sponsors an orphan will be like this in Paradise” – and he gestured with his index and middle fingers, holding them slightly apart. Sahih al-Bukhaari, 4998
But it must be pointed out that when these orphans reach adolescence, they must be separated from the wives and daughters of the sponsor. Good should not be done with one hand and evil with the other. It should also be noted that the one who is sponsored may be an orphaned girl and she may be beautiful and may become attractive before adolescence, so the sponsor must watch his sons lest they fall into doing haraam things with the orphans, because this could happen and be a means of causing mischief which it will be difficult to put right.
It is encouraged to sponsor orphans, for this is something that is rarely done except by those whom Allaah has made righteous and caused them to love good and feel compassion for the orphans and the poor. 
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