Having a big ego is when someone thinks he is more important than most or all other people, that his wants and needs are the most the important, and that everyone else's "less important" lives should take a back seat to "all-important him".
Two-year-olds are generally people with big egos, but as they (hopefully) mature, they become able to see that they are "part of the world", rather than "ruler of it" or "star of it". Sometimes parents don't do a very good job of helping their child grow past the egotistical thinking of a two-year old while also not "pushing them down" and making them feel like "nothing".
A person with a healthy "size" ego knows he is as important, but not more important, than everyone else. Depending on the person's level of altruism, someone may know he's as important as everyone else but choose to place others ahead of him for altruistic reasons.
People who have a certain type of "mental/emotional" maturity generally operate on something less self-involved than their own ego. In fact, part of maturing is growing beyond our own ego to a large extent (although we'll always have some). Over-inflated egos could be said to be a matter of immature, lack of perspective, misplaced values, or being generally misguided.