Decorations keep bettas entertained when you aren't there to entertain them. Lots of plants, caves, and other decorations give them a 'territory' to patrol and explore, and stimulates their little fishy brain to mimic behaviors that keep them busy and active in the wild.
This is also why redecorating and moving around the objects in a tank when you do a complete water change (or anytime you take the betta out of the tank) keeps them from becoming complacent and bored with the same 'territory'.
Some bettas also do well with company, though not necessarily where they can get to them. This provides them with external stimulus. It's one of the reasons why I like keeping my males in a divided 10 gallon. They keep each other occupied.
Training Bettas to do Tricks
That's a great page about one woman's experiment in teaching a betta several tricks, made an interesting read.
YouTube - Betta fish training session
An entertaining video about a betta being taught to swim through a hoop
YouTube - Jumping Betta Fish
Jumping betta video, also somewhat amusing.