When on a balance board, you have many muscle groups all working together to keep you upright. As your muscles work, they burn calories. The warmer they get, the more calories they burn. The longer you can stay balanced, the warmer they will get.
This creates an exponential effect when it comes to burning calories on a wobble board. You will be burning more calories per minute once you reach the two-minute mark than you were when you were on the board for only one minute.
Plus, muscle needs calories as fuel. As you build muscle with regular use of your board, your muscles will burn more calories even when you aren't working out.