When players log out of the server, their items are left behind as non-solid floating entities, with the owner's name attached. Other players can punch the floating items repeatedly (or "dig" them) to knock them loose and grab them. Players logging back in will have the same items they had when logging out, minus anything removed by other players.
The intended use is for cooperative games, to prevent a player who has to leave suddenly from leaving with a bunch of supplies needed by the rest of the team. There may also be PvP applications (e.g. to require players to put more thought into theft prevention), but these have not been explored extensively.
You cannot insert items into an offline player's inventory, including returning items you borrowed. Items need to be left somewhere the offline player will find them when next logging in, and that player will need to voluntarily pick them up.
When using a protection mod, items cannot be stolen from a player who is standing inside their own protected area, unless that area is also accessible by the stealing player.