The 3rd installment of The Sims franchise. It is a life-simulation, where you create characters, known as Sims, and live out their lives.
You get to choose how your Sim looks, what their personality is, their family size, their house, everything about their lives is created by you. You must also pay attention to your Sim's needs and wants. Needs are what keep your Sims alive and/or well (hunger, bladder, hygiene, etc). Wants are things that your Sims want to do, which you can either acknowledge or deny. Things like trying out fishing, or try a new recipe, etc.
One of the new features in the Sims 3 is the Open Neighbourhood, which basically means you can go from your house to downtown without loading screen. This was not possible in The Sims or The Sims 2.
Now, for some of the bad aspects of The Sims 3.
In general, EA (the The Sims creator) is known for creating MANY expansion packs for The Sims games. They even create "item packs" which are packages of new items like furniture, or hairstyles for Sims, etc.
Even worse, in The Sims 3, they have also implemented this new Sims online store where you buy items with real money over the internet. Many items are purposely taken out of The Sims 3 so that you have to buy them through either the endless expansion packs, or the Sims online store. Honestly, EA loves to take all of it's LOYAL customers' money.
If you want more info. on this game, see The Sims
or just google it.