Just like Animal Crossing for the Gamecube, with a few additions and surprises.
Animal Crossing Wild World is pretty fun. Basically you are a boy or girl who arrives in a new town, is given some new digs (and some debt to pay it off). There are lots of ways to earn money, including planting fruit trees, fishing, bug collecting, trading in the turnip stock market...
In addition to amassing wealth, you can get bigger houses, help the museum collect fish, bugs, fossils and other artsy type stuff. You can participate in fishing tournaments, do tasks for other townsfolk and a number of other rather tame activities.
As a result of the "no pressure" type play, the game is rather relaxing, and I've had a good amount of fun figuring out the best ways to rake in the bells, the unit of currency in Wild World.
A big addition to the game in this version is the wifi capabilities. You can allegedly connect with other people out on the net, and visit their towns or invite them to yours. I say allegedly because I have yet to be able to do so, in about 2 weeks time of playing.
The problem with the wifi is that you need to share friend codes in order to visit towns. In addition you are not on the net by default. If you want to invite guests, you have to visit a guard every time you play. Also, if you want to go out to another town, you have to visit the same guard and tell him "I want to go out". This is to prohibit roving packs of people you don't know from coming in to your town and chopping down all your fruit trees. While a good security measure, it limits access to those people whom:
A) You share friend codes with.
B) Are playing Animal Crossing at that moment.
C) Who decide to go to the top of the map and talk to the guard to either "Let you out", or "Invite guests".
I have gone on to a website called DSmeet to attempt to connect with other users playing Animal Crossing. Lots of people share friend codes there, but noone is ever online. If you could somehow leave your wifi on and looking for people to connect to, this would be a much better system. A wifi process that seriously gimps your connectivity is no good for anyone.
Aside from this the game is rather fun, but once you have picked all your fruit trees, done any planting you need to do, talked to some towns folk, dug up some fossils and stuff you are pretty much done for the day. So you typically tend to spend time in the game in short spurts every day, which is a good or bad thing depending on how you look at it.