To abrogate means to abolish, do away with, or annul, especially by authority.
This is a key term in studying the Quran. There are some peaceful, tolerant verses in the Quran. But the violent, intolerant ones have abrogated them. The Quran itself explains what to do with conflicting verses. If two passages conflict, it says, the one written later is better than the one written earlier. The earlier passage has been abrogated by the later one.
The bad news for non-Muslims is that almost all the peaceful passages were written earlier, and the intolerant, hateful, and violent ones were written later (read more about this).
The two key abrogation passages in the Quran are these:
2:106 "Whatever of Our revelations We repeal or cause to be forgotten, We will replace them with something superior or comparable. Do you not know that Allah has power over all things? Do you not know that Allah reigns sovereign over the heavens and earth and besides Him you have no protector or helper? Would you question your messenger as Moses was questioned in his time? Those who exchange their faith for disbelief have gone astray from the right path."
16:101 "When We exchange one verse for another, and Allah knows best what He reveals, they say, 'You are making this up.' Most of them do not understand."
Bill Warner writes, "There are as many as 225 verses of the Koran that are altered by later verses. This is called abrogation."
Read an excellent article by the Martel Group, who knew way ahead of the rest of us that Islamic violence and Islamization were a threat to the free world: Abrogation (PDF document).
Another good article on abrogation is here: Abrogation of the Koran, Koranic Contradictions and Muslim Taqiyya. I thought this was interesting (from that article):
Of the Koran's 114 suras (chapters), only 43 are without abrogated or abrogating verses. That is naturally surprising, and so unexpected that few Westerners are aware that significant segments of the Koran have been theologically annulled. Mohammed's non-Muslim contemporaries were just as surprised.
Another good article is Peace or Jihad? Abrogation in Islam.
For more on abrogation, read these selections from the ex-Muslim's site, FaithFreedom.org:
"Abrogation" means the canceling or replacement of one Quranic passage by another. It seems that as circumstances changed during the 23-year period that Muhammad dictated the Quran, the directions and precepts found therein sometimes changed to accommodate new and changing political and military realities, sometimes quite dramatically. Thus, the Quran abrogates or cancels itself in various passages and presents seemingly conflicting statements. Muslims do not view this sort of abrogation as a contradiction, but rather, as improvements to better suit varying circumstances or needs, or to fit Muhammad's religious concepts. For further reading, see the articles below.
The Quran's Doctrine of Abrogation:
Abrogated Verses Of the Quran:
Abrogation in the Koran:
The Problem of Abrogation in the Quran:
Ahmad, Allah, and Abrogation: