Someone who is overly proud and arrogant can be described as boastful. Your boastful classmate is always going on and on about his own amazing achievements and incredible successes.
It's perfectly okay to brag about yourself sometimes. A boastful person just doesn't know when to stop talking about how great they are, or what amazing possessions they own, or how successful they are. If you hear yourself talking pretentiously about your record collection or the many languages you can speak, you'll know you're being boastful. That's when it's time to stop, ask some questions, and give someone else a chance to shine.