The right of habeas corpus (Latin for "produce the body") is the right to challenge the government's authority to detain you and require it to show just cause for your imprisonment. The right of habeas corpus is fundamental to American law; it's the only individual liberty included in the text of the Constitution itself rather than in the Bill of Rights or subsequent amendments.
Senator Arlen Specter and Attorney General Alberto Gonzales recently had an exchange on the subject, reproduced here for your reading pleasure:
Specter: Now wait a minute, wait a minute. The Constitution says you can't take it away except in the case of invasion or rebellion. Doesn't that mean you have the right of habeas corpus?
Gonzales: I meant by that comment that the Constitution doesn't say that every individual in the United States or every citizen has or is assured the right of habeas corpus. It doesn't say that. It simply says that the right of habeas corpus shall not be suspended.