The most obvious definition of bravado, if you look at the word itself, is that it is a showing of bravery. The important part of this definition is that it is a "showing" of bravery, not actual bravery. Someone would be acting with bravado if he claimed he could beat a bear in a wrestling match, but in his heart knew that he couldn't. On the contrary, actual bravery would be attempting to wrestle a bear to save a person in danger (knowing precisely how dangerous it is), not just claiming to be able to in order to show off. Bravado is not a genuine belief.
The subordinate definition of bravado is merely an extension of the main definition. A person can act with bravado in cases where no bravery whatsoever is necessary. For example, a person could say with bravado that they can finish a crossword puzzle in two minutes. This is equivalent to the previous definition because the aim is to project a more able self than is actually true. Bravado is projected confidence in order to affect others' opinions of your strength or ability.
The idea of ego has its roots in the awareness of the self. The most basic definition of the term is simply the self as distinct from the world and other people. When the word is generally used, however, it is used to describe a person's pride in their self. An egotistical person is someone who believes he or she is at the center of every event. A definition of ego with this in mind would be an exaggerated sense of self-importance. Likewise, ego in this sense can mean an appropriate level of pride in oneself. The key difference between this type of ego and bravado is that ego is a genuine belief, even if it is wholly incorrect, and bravado is a projected, not a believed view.
Sigmund Freud split the psyche into three distinct parts. The first of these to develop is the "id," which is the part of our brains that expresses desire. The id may think "I want to have 50 chocolate bars," and decide to steal them from a shop, because the id has no sense of morality or reality. The "ego" is the second part of the psyche that develops, which is the mediator, the "self" as most people understand it. The ego would step in and say, "Perhaps 50 chocolate bars is too many; I should just steal five," because it has a sense of reality but still no morality. The "superego," or the conscience, develops last, and is the psyche's moralist. The superego would step in and say "Stealing is wrong; I should just buy one chocolate bar."