No. You live in a little forest with a beach, a bunch of stores and a few animal villagers. (The forest is randomly created, and the game randomly select the animals that will live in the village)
There's no real objective. You fish, capture bugs, find fossiles, and bring it all to the museum, or sell it. With the money you make, you can build a bigger house and buy decorations for your house, buy clothes, buy gifts to the animals, befriend them...
It uses the real clock, you play on a day by day basis (each new day, the stores have different stuff). There's events (for instance, Christmas, Halloween, etc...) where every villagers celebrate, and you can get unique stuff on those days.
You can visit other players' villages online, but it's not an mmo. It's a slice of life game. You just live your life, have fun, relax, talk to the animals, play with them, customize your character and your house...