A beard is the collection of hair that grows on the chin, cheeks, but not the upper lip, of human beings. Usually, only pubescentor adult males are able to grow beards.
The beard (Arabic: lihya) is defined as the hair which grows on the cheeks and the jaws. It includes the hair of the temples, the growth underneath the lower lip, the hair of the chin, and the hair that grows on the lower side of the jaws. 
O you who have believed, obey Allah and obey the Messenger and those in authority among you. And if you disagree over anything, refer it to Allah and the Messenger, if you should believe in Allah and the Last Day. That is the best [way] and best in result. Quran.4:59 
These are the limits [set by] Allah, and whoever obeys Allah and His Messenger will be admitted by Him to gardens [in Paradise] under which rivers flow, abiding eternally therein; and that is the great attainment. Quran.4:13 
Narrated Nafi': "Ibn Umar said, The Prophet said, 'Do the opposite of what the pagans do. Keep the beards and cut the moustaches short.' Whenever Ibn 'Umar performed the Hajj or 'Umra, he used to hold his beard with his hand and cut whatever moustaches. Ibn Umar used to cut his moustache so short that the whiteness of his skin (above the upper lip) was visible, and he used to cut (the hair) between his moustaches and his beard. (Translation of Sahih Bukhari, Dress, Volume 7, Book 72, Number 780)"
Narrated Abu Huraira: "Allah's Apostle said, 'The Jews and the Christians do not dye (their grey hair), so you shall do the opposite of what they do (i.e. dye your grey hair and beards).' (Translation of Sahih Bukhari, Virtues and Merits of the Prophet (pbuh) and his Companions, Volume 4, Book 56, Number 668)"
Narrated Muhammad bin Sirin: "I asked Anas, 'Did the Prophet dye his hair?' Anas replied, 'The Prophet did not have except a few grey hairs.' (Translation of Sahih Bukhari, Dress, Volume 7, Book 72, Number 782)"
Narrated Abu Sa'id Al-Khudri: "The Prophet said, 'There will emerge from the East some people who will recite the Qur'an but it will not exceed their throats and who will go out of (renounce) the religion (Islam) as an arrow passes through the game, and they will never come back to it unless the arrow, comes back to the middle of the bow (by itself) (i.e., impossible). The people asked, 'What will their signs be?' He said, 'Their sign will be the habit of shaving (of their beards). (Fateh Al-Bari, Page 322, Vol. 17th).' (Translation of Sahih Bukhari, ONENESS, UNIQUENESS OF ALLAH (TAWHEED), Volume 9, Book 93, Number 651)"
Shaykh Ibn ‘Uthaymeen (may Allaah preserve him) said: The definition of the beard as stated by the scholars of (Arabic) language is: the hair of the face, jawbone and cheeks, in the sense that all the hair on the cheeks, jawbone and chin is part of the beard and removing any of it is counted as a sin, because the Messenger (peace and blessings of Allaah be upon him) said: “Let your beards grow,” “Leave your beards alone,” “Let your beards increase,” “Let your beards be full.” This indicates that it is not permissible to remove anything from the beard. But the sin may vary in degree – shaving the beard is worse than shortening it, because it is a more obvious contradiction of the Sunnah.
Al-Muwatta Hadith 49.3
Yahya related from Malik from Said ibn Abi Said al-Maqburi from his father that Abu Hurayra said that the Messenger of Allah (saws), "There are five things from the ‘fitra’ (nature): cutting the nails, trimming the moustache, removing the hair from the armpit, shaving the pubic region and circumcision."
Al-Tirmidhi Hadith 4437
Narrated by Abdullah ibn Abbas (R):The Prophet (saws) used to clip or take something off his moustache, and Prophet Ibraheem, the ‘Khaleel’ (intimate friend) of the Compassionate One, used to do the same!
Sahih Al-Bukhari Hadith Vol 7.780
Narrated by Nafi: Abdullah Ibn Umar said that the Prophet (saws) said, "Do the opposite of what the pagans do. Keep the beards and cut the moustaches short.". Ibn Umar used to cut his moustache so short that the whiteness of his skin (above the upper lip) was visible, and he used to cut (the hair) between his moustaches and his beard.
The Arabic term used for ‘shaving’ is ‘halaq’; while the term to cut or trim in Arabic is ‘Qass’ or ‘Ahfu’…..and in all the guidance regarding the moustache the term used in the hadith is either ‘Qass’ or ‘Ahfu’ (meaning cut or trim) and never ‘Halaq’ (shave).
The scholars and jurists in Islam are almost unanimous in their opinion that the Sunnah is to cut or trim the moustache, rather than shave it completely. 
Shaving the beard results in a series of Islamic violations, as is obvious from Allah's Book and His Messenger's Sunnah. The following is a list (not necessarily comprehensive) of such violations:
Shaving the beard is a disobedience to Allah. The ruler of Yemen, appointed by the Persian emperor Kisraa, sent two envoys to the Messenger (peace and blessings of Allaah be upon him) to summon him. When they came into his presence, he noticed that they had shaved their beards and grew their moustaches. He hated to look at them (because of their odd appearance) and he said: Woe be to you, who told you to do so? They replied: "Our lord! (referring to Kisraa.)" The Messenger (peace and blessings of Allaah be upon him) then said:
Shaving the beard is a disobedience to the Messenger (peace and blessings of Allaah be upon him). In many hadiths, the Messenger (peace and blessings of Allaah be upon him) commanded men to leave alone their beards. These different hadiths have a similar meaning:
Shaving the beard is a deviation from the appearance and guidance of the Messenger (peace and blessings of Allaah be upon him). The Messenger (peace and blessings of Allaah be upon him) used to have a large beard [Muslim]. One should strive to imitate him (S) in his practices, as Allah said (what means):In the Messenger of Allah is a good example for you to follow. [Al-Ahzab 33:21]
Shaving the beard is a deviation from the way of believers. All the prophets (S), the sahbah (Prophet's companions), the great `ulamaa, and the righteous early Muslims of this Ummah (Nation) grew their beards. There is no report of a single one of them ever shaving his beard. Thus, this is their way, and Allah says (in the meaning):
Shaving the beard is an imitation of the disbelievers. This has been emphasized in several hadiths of the Messenger (peace and blessings of Allaah be upon him). For example:
The Messenger (peace and blessings of Allaah be upon him) declared that the women who change what Allah (Tala) has created (such as removing the hair from their faces or filing their teeth or tattooing their bodies) seeking by that to improve their appearance, are accursed by Allah (T). [Al-Bukhari and Muslim]
The beard is a major distinction between men and women. Shaving it removes this distinction, and is thus a means of imitating women. The Messenger (peace and blessings of Allaah be upon him) said:
The Messenger (peace and blessings of Allaah be upon him) mentioned ten qualities as indicative of a good, clean nature [Muslim]. Two of these qualities are to trim the moustaches and to grow the beard.