You play against each other in the same town basically competing for the best stats, although there are a few game modes like the 1st person to fail an emergency loses or 1st person to fail a VIP visit loses, there are some others too. You start off with a small building each at opposite ends of the map then when you need more space you each bid for new plots. If you want to sabotage your opponent's hospital you can drop a Litter Bomb in their hallways which explodes after a minute or so throwing crap all over the place and causing rat infestations and whatnot :)