Immodest means showing off or drawing too much attention to yourself and your accomplishments, or (in a different sense) not covering your body in a way your culture considers appropriate.

When someone brags constantly about their test scores, their athletic abilities, or how much money their family has, they're being immodest. They're putting themselves forward in a way that makes others uncomfortable. If you solve a difficult problem in class, you can feel proud without announcing to everyone how smart you are. That's the difference between quiet confidence and immodesty.

The opposite is being modest: recognizing your strengths without constantly advertising them, and letting your actions speak for themselves. Someone modest might say “I worked really hard on that project” rather than “I'm obviously the best artist in the whole school.”