Those are experienced player badges. They’re used to identify players with certain levels of experience so you know who you’re up against. These badges appear alongside the player’s username. Experienced players can’t enter contests specifically excluding such players, like beginner only contests. A player will be tagged with an experienced or highly experienced badge according to the following criteria:
Experienced Player (blue star in white circle) — Any user who has played in 500 or more contests, OR has won a total of $2,500 or more over a span of six or more contests.
Highly Experienced Player (white star in blue circle) — Any user who has played in 1,000 or more contests, OR has won $1,000 or more in a single contest four or more times.