Someone who is egotistical is full of himself, completely self-absorbed. Like the egotistical actor who blocks the audience's view of every other actor in the play during the curtain call so that he can hog the applause.
The prefix ego refers to a person's sense of self, or self-importance. To be egotistical is to have an inflated view of your self-importance — basically to think you're better than everyone else. You might express this egotism by constantly reminding your friends that you have a fantastic figure or a magnificent mind.