The two white and black stone on top of each other ( / / / ) in the running games list indicate, what your color in the game is and who is to play next. When you place your mouse (cursor) over the image, a hover text is shown describing the meaning.
 
The color of the top stone shows your color.
The color of the stone below shows which color has to make the next move.
So, when both colors are the same, it's your turn!