Games don't look so hot all the time mainly because of texture resolution and compression techniques. I will add that resolution of the meshes that are used in games could be higher res, which would give you smoother looking edges around things.
Higher anti-aliasing (aa) would clean up the edge quality of the meshes regardles of the mesh size. What it does is resample all goemetry edges to a certain level. AAx2 would do 2 passes of the edges, AAx4 would do 4 passes, so forth and so on. This requires processing power, and if you throw the cpu at that it cant be doing something else. I believe this function is handled on the graphics chip though, but if youre overwhelming it with AA routines, it might be taking a performance hit trying to do something else. I'ts all a balencing act.
The main issue though is the compression on the texture maps. I assume you've seen a really compressed jpeg image before, or even a highly compressed avi, mpeg or mov file. It's the same deal. Images with high compression on them tend to look muddy or chunky. Images with low or no texture compression on them look clean and sharp.
Another thing to keep in mind is that when you get a ton of models in a game onscreen at the same time, you have to share the texture memory in the console with all of the models and geometry. If you add in things like reflections and refraction (bending of light hrough transparent objects) you need to create multiple versions of the same thing.
Not to mention any other effect thats thrown in there like glows and shading types to make things look dull or shiny.
A related issue to visual quality is frame rate. When you have too many things onscreen at the same time, probably using more texture memory than available, you get the console slowing down. While it isnt solely a texture problem, it is related.
