Once you enter a Puzzle level you'll be presented with a Goal to complete in that level, it could be racking a certain amount of points, or destroying a certain number of specific pieces.

Then you'll have to swap pieces to form combinations of 3, 4 or 5 pieces of the same color.
Combinations of 4 and 5 pieces will give you special pieces called EXPLOSIVES.

When combined with other pieces of the same color the EXPLOSIVES burst into different patterns that will help you clear more pieces on the board and achieve your objective faster.