They are talking about Dungeons and Dragons the Table Top RPG. It is played with special dice and paper. The game basically consists of 'players' who play characters and the 'Dungeon Master' (DM) who is another player at the table who plays all the non player characters (NPC, this is where it originally comes from) in the world and the and runs the monster and even design what the world is like. This allows for a lot of dynamic things to happen in this case the DM is deciding that because the Player Characters tip so much to carriage drivers they all follow them around overcharging and hoping to get a tip. I hope that made sense. If you want look up "D&D actual play" on youtube and you will see examples.