The act of logging on to the xbox website and checking who's online to determine whether or not you should log on "offline" to avoid chat and game invites from annoying people.
Alternatively can be used to find out who's online that you overly enjoy the company of. In which case you become the 360 screened.
Matt: Hey get online, i wanna play modern warfare 2!
Joe: Hang on, lemme 360 screen to make sure that one guy that always wants to private chat me isn't on.
Genericgamertag190: I hope Joe isn't 360 screening. I haven't talked to him in forever.