As you participate in matches you will see a green bar underneath your wrestler's picture. This is your experience bar. When you fight in matches you earn experience and when you reach a certain threshold, your wrestler will gain a level. Gaining new levels gives your wrestler more Attribute Points to use to make them more powerful. Winners gain more experience than losers, also beating higher-level wrestlers earns more experience than beating lower-level ones.
You can hover your mouse over the Experience Bar to see how close you are to hitting the next level.