The "Days of Future Past" is a divergent time period in Marvel Comic's history where the Earth has been dominated by the mutant-hunting machines known as Sentinels. In this alternate reality, the Sentinels continued to grow in power and intellect and eventually came to the conclusion that the only way to eliminate the mutant "threat" was to exterminate not only mutants but normal humans as well in order to prevent any future mutant births. The ensuing war led to the Earth being reduced to a barren wasteland, with whole cities reduced to rubble and mutants being routinely rounded up for systematic destruction. Some mutants are kept alive and forced into slavery, their powers surpressed by collar devices. Others are experimented on, allowing the Sentinels to develop and adapt new abilities, essentially evolving.
In various Marvel comics and TV shows, the X-Men have attempted to alter the course of history to prevent this future from occurring. In most instances they have succeeded and in others have merely postponed it (repeatedly), changing various aspects each time but never managing to create an ideal future.