You can earn a medal by placing first, second, or third in a tournament!
To see what medals you have, hover over the Chess.com logo in the left menu, and click 'awards':
From there, click on 'Medals' to see all the awards you have earned!
The medals will be separated into stacks (If you've won multiple of one kind) and separated by kind of tournament. To see all the medals in a stack, click on the stack:
You can then scroll through to look at each medal. Medals often have their own custom image unique to the tournament they came from.