Habeas corpus (Latin for "You have the body") is a writ used to seek relief from unjust detention by the government. Its main purpose is to make sure that the feds can't just throw people in jail because they feel like it — they need a good reason.
Some people suspend habeas corpus when they feel like it, like Abraham Lincoln during the American Civil War. (Of course, there is an explicit provision in the US Constitution for the suspension of habeas corpus during times of rebellion and insurrection, such as the Civil War, although the Supreme Court ruled that only Congress, not the President, could do this.)
The George W. Bush administration conveniently ignored the entire notion of habeas corpus, something along the lines of "we need to suspend it to fight the terrorists, if you're not with us you're with the terrorists, you should be deported to France" nonsense. Interestingly, the purpose of habeas corpus is to prevent that kind of thing. Fortunately for silly civil libertarians, the Supreme Court ruled that even foreign nationals in Gitmo have the right of habeas corpus.