It's quite a simple concept. You have a 5x5 grid of cards that either contain a number of a Voltorb. Down the side and bottom it tells you how many Voltorbs are in that row or column.
If you uncover a Voltorb, you lose. You win the level by uncovering all the x2 and x3 multiplier cards.
See here for strategies: Is there an easy way of winning the Voltorb Flip minigame?