What does Put away do?

Put away, on Account, takes a character out of your account: it leaves your lists and its page at once. Nothing of it is deleted when you do, and you can bring it back with one click for 30 days; after that it stays put away, and Homerealm may delete it. The terms say when.

It is not Keep off Homerealm, which hides a character from other players' pages.