Angel Tarragon
Dawn Dragon
Please pardon my stupidity but what exactly are all the things can a hero do with an action point?
Note tag; yes.Is this strictly a 4E question?
1) Gain an extra action (attack, move or minor). Some feats and abilities give you extra benefits when you do this.
2) Anything else that a particular paragon path ability or feat allows you to do. For example, the Arcane Mastery feat allows you to spend an action point to regain a daily spell.
Starglim was mostly right, but maybe not very clear with answer 1. You simply gain an extra Standard action. This is usually going to be an attack, but if you want you can downgrade it to a Move action or even a Minor if you feel so inclined. So the simple answer is "anything you can do with a Standard action".
As for answer 2, quite a few magic items also let you gain some benefit instead of gaining the extra Standard Action.