Stars under Player Ranks?

As a player levels up, their portrait gets more flair every 10 levels.

At level 100, their flair resets but they earn a bronze star.

This repeats every 100 levels, so that at level 501 they've earned 5 bronze stars.

At level 601 it resets to a silver background, with 1 silver star at 701 and 5 silver stars at 1201.

At level 1301 it resets with gold backgrounds/stars.

Source.

Your level is more or less just an indicator of how much you've played.

This is the player's level, 1-100. Each star in addition represents 100 previous levels the player achieved. A player with 2 stars and a level of 30 is level 230.

Level is based on experience and nothing more. It has no relation to skill or any other statistics other than how much experience the player earned. This makes it mostly correlated to simply how much they've played as you get experience for winning and losing nearly the same.