The action or process of repenting especially for misdeeds or moral shortcomings. 
Repentance Means turning back from disobeying Allah to obeying Him.
Allah (Glory be to Him) says: “And all of you beg Allah to forgive you all, O believers, that you may be successful” Qur’an.Surah Noor 24:31
Allah (Glory be to Him) is Kind to His slaves, and His mercy encompasses all things. Whoever repents after doing wrong, Allah (Glory be to Him) will accept his repentance, for Allah (Glory be to Him) is Forgiving and Merciful as is said by Allah (Glory be to Him) in Qur’an, [interpretation of the meaning] “But whosoever repents after his crime and does righteous good deeds (by obeying Allah), then verily, Allah (Glory be to Him) will pardon him (accept his repentance). Verily, Allah is Oft Forgiving, Most Merciful.”Qur’an.Surah Ma’idah 5:39
The sins, mistakes or crimes of a person may not deserve to be forgiven but those who believe in Allah (Glory be to Him) are always hopeful for His Mercy, as Allah (Glory be to Him) says [interpretation of the meaning],“…your Lord has written (prescribed) Mercy for Himself, so that if any of you does evil in ignorance, and thereafter repents and does righteous good deeds (by obeying Allah), then surely, He is Oft-Forgiving, Most Merciful” Qur’an.Surah An’am 6:54. 
O my brother who has fallen into sins, do not despair from the mercy of your Lord, for indeed the door to repentance is open until the sun rises from the west. The Prophet (sallAllaahu 'alayhi wa sallam) said: "Verily, Allaah extends His hand out at night in order to accept the repentance of the sinner by day. And He extends His hand out during the day in order to accept the repentance of the sinner by night, until (the day) when the sun will rise from its west." Sahih Muslim 2759
Making mistakes and falling short are undoubtedly part of human nature and no one will be free of shortcomings in his obedience to Allah (Glory be to Him), or free of mistakes or forgetfulness or sins. All of us fall short, commit sins, and make mistakes. We are not infallible. Hence the Prophet Muhammad (May Allah honour Him and Grant Him peace) said: “By the One in Whose hand is my soul, if you did not commit sin Allah would do away with you and bring people who would commit sin then pray for forgiveness.” Narrated by Sahih Al Muslim 6621.
And He (May Allah honour Him and Grant Him peace) said: “Every son of Adam sins and the best of those who sin are those who repent.” Narrated by Tirmidhi 2499; classed as Hasan by al-Albaani.
The Prophet Muhammad (May Allah honour Him and Grant Him peace) said: “By Allah (Glory be to Him), I seek the forgiveness of Allah (Glory be to Him) and I turn to Him in repentance more than seventy times each day.” Narrated by Sahih Al Bukhari, vol 8:319.
It was narrated from Abu ‘Abd al-Rahmaan ‘Abd-Allaah ibn ‘Umar ibn al-Khattaab (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) said: “Allaah will accept the repentance of His slave so long as the death-rattle has not yet reached his throat.” Narrated by al-Tirmidhi, 3537; classed as hasan by al-Albaani. 
Hadith E Qudsi on repentance
It was narrated from Abu Sa’eed Sa’d ibn Maalik ibn Sinaan al-Khudri (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) said: “There was among the people who came before you a man who killed ninety-nine people. Then he asked about the most knowledgeable person on earth, and was directed to a hermit, so he went to him, told him that he had killed ninety-nine people, and asked if he could be forgiven. The hermit said, ‘No,’ so he killed him, thus completing one hundred. Then he asked about the most knowledgeable person on earth and was directed to a scholar. He told him that he had killed one hundred people, and asked whether he could be forgiven. The scholar said, ‘Yes, what could possibly come between you and repentance? Go to such-and-such a town, for in it there are people who worship Allaah. Go and worship with them, and do not go back to your own town, for it is a bad place.” So the man set off, but when he was halfway there, the angel of death came to him, and the angels of mercy and the angels of wrath began to argue over him. The angels of mercy said: ‘He had repented and was seeking Allaah.’ The angels of wrath said: ‘He never did any good thing.’ An angel in human form came to them, and they asked him to decide the matter. He said: ‘Measure the distance between the two lands (his home town and the town he was headed for), and whichever of the two he is closest to is the one to which he belongs.’ So they measured the distance, and found that he was closer to the town for which he had been headed, so the angels of mercy took him.” (Agreed upon).
According to a version narrated by Muslim (2716): “He was closer to the righteous town by a handspan, so he was counted among its people.”
According to a version narrated by Muslim: “He leaned with his chest towards it”. 
"O 'Ibadi (My slaves) who have transgressed against themselves (by committing evil deeds and sins)! Despair not of the Mercy of Allâh (Glory be to Him), verily, Allah (Glory be to Him) forgives all sins. Truly, He is Oft-Forgiving, Most Merciful. Qur’an.Surah Zumar 39:53 .
Allah (Glory be to Him) is Kind to His slaves and loves those who repent. He accepts their repentance. The Prophet Muhammad (May Allah honour Him and Grant Him peace) said: “When a person repents, Allah (Glory be to Him) rejoices more than one of you who found his camel after he lost it in the desert” Agreed upon. Narrated by Sahih al-Bukhari, vol 8:321.
Those who committed Faahishah (illegal sexual intercourse):
“And those who, when they have committed Faahishah (illegal sexual intercourse) or wronged themselves with evil, remember Allah (Glory be to Him) and ask forgiveness for their sins; — and none can forgive sins but Allah (Glory be to Him) — and do not persist in what (wrong) they have done, while they know” Qur’an.Surah Ale Imran 3:135
Allah (Glory be to Him) calls to repentance those who committed the gravest form of shirk and sin, those who say that Prophet Eesa (peace be upon Him) is the son of God – exalted be Allah (Glory be to Him) far above what the wrongdoers say. Allah (Glory be to Him) says (interpretation of the meaning): “Will they not turn with repentance to Allah and ask His forgiveness? For Allah (Glory be to Him) is Oft-Forgiving, Most Merciful” Qur’an.Surah Ma’idah 5:74.
Allah (Glory be to Him) opens the door of repentance to the hypocrites, who are worse than the kuffaar who openly show their kufr. Allah (Glory be to Him) says (interpretation of the meaning): “Verily, the hypocrites will be in the lowest depth (grade) of the Fire; no helper will you find for them. Except those who repent (from hypocrisy), do righteous good deeds, hold fast to Allah (Glory be to Him), and purify their religion for Allah (by worshipping none but Allah, and do good for Allah’s sake only, not to show off), then they will be with the believers. And Allah (Glory be to Him) will grant the believers a great reward” Qur’an.Surah Nisa 4:145-146. 
Sincere repentance is not merely the matter of words spoken on the tongue. Rather, the acceptance of repentance is subject to the condition that the person gives up the sin straight away, that he regrets what has happened in the past, that he resolves not to go back to the thing he has repented from, that he restores people’s rights or property if his sin involved wrongdoing towards others, and that he repents before the agony of death is upon him. Allah (Glory be to Him) says (interpretation of the meaning): “Allah accepts only the repentance of those who do evil in ignorance and foolishness and repent soon afterwards; it is they whom Allah will forgive and Allah is Ever All-Knower, All-Wise. And of no effect is the repentance of those who continue to do evil deeds until death faces one of them and he says: ‘Now I repent;’ nor of those who die while they are disbelievers. For them We have prepared a painful torment” Qur’an.Surah Nisa 4:17-18.
Sincere Repentance: Must meet five conditions (in order to be accepted), which are:
According to Imam Al Nawawi
What is meant by repentance is returning to Allah (Glory be to Him), giving up sin and hating it, and regretting falling short in obedience to Allah (Glory be to Him). Al-Nawawi (may Allah have mercy on him) said: Repentance is essential from every sin, even if it is something between a person and Allah (Glory be to Him) and has nothing to do with the rights of another person. There are three conditions of repentance:
1- You should give up the sin
2- You should regret having done it
3- You should resolve never to go back to it.
If one of these three is missing, then your repentance is not sincere. If the sin has to do with the rights of another person, then there are four conditions: the three mentioned above and restoring the rights of that person. If it is money or property, etc, it must be returned to him; if it had to do with slandering him etc, then you should allow him to insult him in return, or ask for his forgiveness; if it had to do with backbiting about him, then you have to ask for his pardon. It is essential to repent from all sins; if a person repents from some, his repentance from the sins from which he repented is valid – according to the scholars who follow the right path – but he must still repent from the rest as well. 
 Written by Muhammad As-Saalih Al-'Uthaimeen 4/17/1406, Sifat Salaat-in-Nabee (pages 49-51), target="_blank" al-Ibaanah.com
Written by Muhammad As-Saalih Al-'Uthaimeen 4/17/1406, Sifat Salaat-in-Nabee (pages 49-51), target="_blank" al-Ibaanah.com