The holy month of Ramadhan is an excellent opportunity to have one's sins forgiven. Allah's blessings and mercy are so abundant in this month that anybody who truly repents in it, becomes as free of sins at the end of the month as when he was born. It is a glorious chance offered to us by the Almighty, a chance to cleanse and purify ourselves from the filth of sins and evil. The Holy Prophet has advised believers: O people . . . your back is breaking under the heavy load of your sins, so prostrate yourself before Him (in Ramadhan) for long intervals, and make it lighter.
It is a proof of the love of the Almighty that each year he gives us a chance to clean our record and make a fresh start. Contrary to those who think that Allah is strict and harsh, that He will punish us as soon as we err, Allah gives us many chances to undo the wrong we have done towards Him. The month of Ramadhan is the best of these chances. All the duas for this month teach us to plead for forgiveness and deliverance from the punishment. One who recites these duas sincerely, and is truly repentant, is assured of forgiveness.

The Holy Qur'an says about seeking forgiveness:

And hasten to forgiveness from your Lord, and a Garden the extensiveness of which is the heavens and the earth, prepared for those who guard against evil. (3:132)
And whoever does evil, and oppresses his soul, then seeks forgiveness of Allah, he will find Allah to be Forgiving, Merciful. (4:110)
Will they not turn to Allah and seek His forgiveness, and Allah is oft-forgiving, Merciful. (5:74)
The following Hadith talk beautifully and eloquently on Istighfar (seeking forgiveness):
Fortunate is the person who finds in his record of deeds a lot of seeking forgiveness. Holy Prophet (s)
The similitude of Istighfar is like the leaves on a tree. The tree is shaken, and the leaves fall off. Imam Ridha (a)
Fragrance yourselves with Istighfar so the stench of sins does not disturb you. Imam Ali (a)
Seek forgiveness abundantly, for Allah has not taught you how to seek forgiveness except because He wishes to forgive you. Holy Prophet (s)
Necessity of Istighfar in the life of a believer
When Allah created the human being, He gave him the faculty of good and evil. The human is free to choose his actions. He can decide to do a good deed, and stay on the right path. Or he can decide to do an evil deed and disobey his Lord. He has two sides to him; the intelligence and conscience that guide him towards good, and the evil soul that invites him to do wrong. The status of the human being with Allah depends on the type of actions he chooses to commit. The record of deeds he commits in this world will determine his end, whether in Heaven having earned the pleasure of Allah, or in Hell, deserving of the wrath and displeasure of Allah.

What happens when a human being sometimes chooses wrong, submits to his evil soul and ignores the dictates of his conscience? Is he doomed to forever carry the burden of that sin? Knowing that human beings were prone to slip, Allah in His immense mercy and wisdom, has opened the door of Istighfar for His servants, the door of seeking forgiveness after a sin. So whoever commits a sin, but repents and wishes he had not committed it, and knows that he will not do it again - at least will try never to repeat it again - can enter that door, and have the sins erased from his record.

Istighfar is the weapon of believers against the Shaytan who tries to lead them into Hell through inviting them to sin. According to a hadith of the Holy Prophet (s), Iblees declared to Allah that he would continuously try to lead humans astray so long as they were alive. Allah answered that He would continuously forgive them so long as they sought His forgiveness.

The best time to seek forgiveness is during the early hours of the morning before dawn. That is a very special time, when all duas are accepted. The Holy Qur'an describes the believers as those who seek forgiveness at the time of dawn.

The holy month of Ramadhan is a time when there is a general amnesty for sinners. Allah invites the sinners to come and seek His forgiveness. This is an opportunity that must not be missed, for no-one knows if he/she will be alive for the next year. When a criminal is told that the government is issuing pardons for those who seek it, to commemorate a happy event, he will jump at the chance to avoid punishment. He can save himself years in jail, a lot of misery and torture, by seeking pardon. It is a golden opportunity which no sensible person would miss. Similar is the case of the sinner who has disobeyed his Lord. He is a criminal, and when Allah offers a special pardon, the sinner seizes the chance. He would like to erase his sins and relieve himself of the burden of disobedience.