1.VerbTo sign one's name as an indication that one is leaving some location; to take some action to indicate one is leaving a secured program or web page on a computer.
"He was the last person to sign out of the building that night.; After making the necessary edits, always sign out of the system."
2.VerbTo remove (something) and take (it) into one's possession, having registered or signed for it in some way as a record of possession and a promise to return it (e.g., by your signature or log-in credentials).
"If you want to take a book home from the library, you must sign it out.; To sign out a book, you must present your library card to the clerk."