The Player Bar is used to give a visual indication of the current state of the game so you can see at a glance what's happening with the game when looking at any of the game list views. In addition, hovering over a box on the player bar will display the player's name and clicking the box will navigate you to the player's profile.
While games are waiting for players to join, the Player Bar shows the colors of the players that have joined as well as the empty slots available. The empty slots are shown as blank white squares at the end of the bar.
Here, the game has recently started. The black dot in the middle of the orange square indicates your position in the game (Note: The dot may be white depending on your player color). The white bar underneath the third square is the turn indicator. This means that it is currently the green player's turn. Note that for some game play types it can be more than one player's turn at once, so keep an eye out for the turn indicator appearing under your player square.
Here, the player bar indicates that the yellow and red players have both been eliminated from the game and it is currently your turn.