Megalomaniac, the first respondent, gave a perfect answer.
But his answer also defines "ego" and "egotism" in much the same way that all laymen do.
I am a layman, myself, so I cant give a perfect answer... but I do know that psychologists and therapists define ego very differently.
In fact, they usually define it in nearly an opposite way that laymen do.
As it turns out, having a "big ego" is actually a good thing. Having a big ego is what Megalomaniac refers to as having a balanced ego.
In layman speak, when someone has a "big ego" it usually means that they over compensate for a lack of ego. Having a genuine big ego, as psychologists define it, means that you have a healthy and confident sense of self. You dont need validation from anyone.
People act egotistical to portray more confidence than they actually have. So those who act like they have a big ego (layman) actually do so because they have a small ego (psychology)... its an overcompensation to gain the illusion of confidence. They are deluded into believing that if others see them as self-confident, they will develop real self-confidence.