The better question is "What can't you do with AE?"
AE is a compositing and animation tool. Yes, AE can do editing...it's a little faster to do it in Premiere or Final Cut though.
AE can take a layered PhotoShop, Illustrator doc and enable you to animate any layer's properties, ie. opacity, scale, rotation, position, blur and all the PS filters over time...and that's just the beginning. Take a look around, with the proper resources and footage, you can literally create anything...movie trailers, intro credits, special effects, green/blue screen mattes, title effects, 3D compositing and more.
All the TV show intros on TV can be created in AE.
Go to Adobe.com and look at their Affter Effects Galleries.
Good luck and be creative,
Pixel