An actual object; they used to make doormats that said "welcome" on them. A proverbial thing that implies some sort of indicator as to whether someone or something is welcome or not. Throwing a party for your new neighbors could be considered putting out the welcome mat for them. It can be used with sarcasm, as in someone trying to set up an ambush would put out a "welcome mat" of some sort that would indicate to the target that everything is right with the world, and no, heavily armed men bristling with weapons are not going to jump out of the shadows and beat them to a bloody pulp.