Medals are simple "awards" that you earn by doing some particular things. These medals are shown and announced in-game in the moment when you get them. When a player gets one of them, the relative icon will appear over his head for a while. This happens in any matches you play. Those of them that you get in Single Player Deathmatch mode (and only in that mode!) are also shown when the match ends, and are stored and shown in the "Single Player Deathmach" menu everytime you enter it.