That’s points for individual piece progress, those can be gained in daily shop actions or (mainly) from cb-s.
You get power points on certain pieces, those points are accumulating, and in one beautiful moment when power points on one chessman reaches number X, you can upgrade it immediately & freely by pressing the button.
- For 1st level: reach 40 points, then wait for getting or buying Ability for this piece;
- For 2nd level: reach 70 points;
- For 3rd level: reach 100 points.
Note that you spend all piece’s points when it takes new level.
In the shop, you can buy some points for certain piece(s) or slightly greater number of those for random one(s).