The clock ticks by in Animal Crossing but nothing really happens unless you are playing. The game uses the clock to determine what events happen in the game. This can be the appearance of a NPC, a festival, the season or just what the other NPC's are doing.
I'm really glad there is no virtual upkeep like a Tamagotchi. Cutsie graphics and all it's an entertaining way to spend a couple of hours.
I just figured out how to plant a money tree!

Really though I have the most fun being able to interact with my daughters character (though indirectly). She gets a kick out of seeing the letter's I've sent her. Plus I can mail her gifts as well. Fun stuff.