I'll try to explain it as simple as I can.
It's a sandbox sidescrolling platform game with 3 levels of depth. All the levels in single player can be created by anyone because of the powerful and intuitive engine. Everything is built around the physics and no matter how skillful you are at it, it's just fun. It's also extremely polished for a sandbox game.
One of the huge things is the charm of the game. The style and music really make it. You play as a "sackboy" and as you play through single player you collect items for your sackboy (and also items for creating levels) and you can dress it up how you want. You can control it's emotions very easy and even his arms to wave or punch depending on the set emotion.
The last big thing is the online. They really made it sleek as hell. You can download other people's levels, play the single player levels with up to 4 people, or play the community created levels with friends. It's all free and . (you can also play co-op offline)
This is the best way I can summarize it but it's really hard to even scratch the surface on how awesome the game is without playing it. If you have a PS3, you need to have this game.
This thread explains it best - http://www.neogaf.com/forum/showthread.php?t=338867
This is one of the amazing levels someone made before the servers went online - http://www.youtube.com/watch?v=aBJlkpTIw48
pinkpanther - Nothing at all like The Sims. I don't even understand how you made that connection.
urgannagru - ughhhh.