AI and physics are largely processor-driven. The Wii couldn't handle several of the 360/PS3 games and their complicated AI and physics.

basically AI and having tons of things on the screen at the same time doing different things.

It helps to create more challenging AI, that try and outflank you etc, and is also used to create bigger levels and more enemies/allies, I guess also to reduce the loading times that would otherwise come with better graphics. Also the physics in things such as racing games must be challenging aswell.

well, you just should wait E3, it`s only 6 weeks, maybe there you will see something or maybe not. =))

The processing power in the PS3 and the 360 allow for stronger AI, more complex interactions, and more of well everything. Take Dead Rising, note the thousand zombies in each room? That is only allowed because there is so much processing power in the 360. The PS3 has around double that, in processing power, it would have more but one of the processors is special. I forget how it's special, but it's not used the same as the others. one of them may or may not work depending on random chance (Cell Processor factory standards allow for 1 of the 6 processors to not work. It is very difficult to have one with all 7 working processors due to the fact that only 10-20 percent of the processors work). Anyways, the PS3 processing power is very difficult to take full advantage of because you have to invest a lot of money in taking advantage of it. Lair is one game that should do this though. At any one time you can have thousands of dragons flying through the air with complex AI, and thousands more soldiers on the ground shooting arrows and such. Lair would be do able on the 360, but they would have to change that to hundreds, and not thousands of things on the ground and in the air. I will say though that you will never see it on the 360 because it is being developed by a Sony second party development team.

Think of creating emotions. Compare, as a example, a game made 20 years ago with Mass Effect: Sound: In case you do have a good sound system at home a big explosion gives you the feeling to be directly in the game. Compare that with the "bleep" of Pong. Graphics: Characters in the game show emotions. Some years ago it was not possible to show that visually. The emotions were expressed by text or sound. Or think about the situation in Resident Evil when the dogs were jumping out of the window. It was really threatening and possible because of the graphical capabilities of the PS1.

AI in of itself isn't all that process intensive, from what I've heard. It's merely coding, and the way it's streamlined and branched out to give the AI more routines. (Relaying from what others have said.) Handling many more characters on screen, each with their own complex AI, possibly. But AI lately in games has been abysmal at best. Physics and more screen activity is at least much more noticeable for the time being, there's games that show that off.

Darkd is  all wrong....

 the cell processor has 9 cores, one is a multi purpose processor like the one in a pc, is called PPU, and it has 8 little coraes that he controls called SPE. The thing is, specific function processors are super fast e.g GPU but they  only work to render graphics, they do that super fast, a normal processor takes ages to do what a GPU does in a flash. i work on 8-bit processor, DPS and  FPG, the last 2 are a kind of IC that do spesific thing but very fast, the thing is SPUs are some kind of hybrids, that are super fast( not as a GPU) but very fexible(not as much a a general purpose CPU), and on top of that they are all in the same chip, that makes comunication between then very fast.

the cell processor in the PS3 has 1 SPU disabled to produce them faster, and another dadicated to the PS3 internal OS, so developer dont have acces to it, developers only have acces to 6 SPUs and the PPU cus the PPU is what controls the comunication to devices outside of the chip.

Another thing, where did DARKD got that only 10- 20% of processor work? , that is such a lie, sometimes some   feature in a processor does not work, when than happends that one is  sold  whit another model number and little cheaper. When a SPU  has  problem IBM puts it in one of the blade server they sell , they dont throw an entire procesor to the trash thats a lie.

 Another thing is that in PS3 can handle phisics engines like the Havok 4.0 engine and works faster  whit it than a hi-end PC,  that means thins move more realistic,  have gravity , bollance, kinetics and all that , those things cant be done in the wii cus you need alot of processing to do that and the frame rate could drop a lot, and since the processor of the 360 are average PC processor they stay behind in physics simulation( a normal proccesor like the ones in the 360 needs 20 machine cycles to do a sin operation, the SPUs need one). The graphics are not what makes the ps3 and 360 diferent, is the support for this kind  of applications that make then more different. 

sorry about my english is not very good.

A faster CPU is good for better AI/Physics/etc. as everyone in this thread has already stated, and the 360/PS3 have an additional advantage: RAM.