What's the definition of writ of habeas corpus?

Habeas Corpus is Latin for "you have the body" - and is historically a writ (or petition) that was intended to be used to force the government to produce a prisoner that they had taken, so that the reasons for their imprisonment and the process leading to that imprisonment could be reviewed and potentially challenged. It is one of the most fundamental rights that a citizen has to control or identify abuses of governmental authority, and thus is one of the most carefully guarded civil processes -- explicitly protected by the US Constitution.