Tetris Attack is all about getting chains and combos to keep your puzzle alive and rain garbage down upon your enemies. One of the more nebulously defined category is the 'skill chain', where you maneuver blocks to form matches while others are still clearing.

Let's say you have this setup here, and you make a clear.

Then you move up, slide out the Heart

With timing so that the bottom part of the puzzle falls before the Diamond on top does

Then, when the Diamond does fall, it counts as a chain!

And, so you can get a better sense of the timing required, I've put together an animated .gif here (4MB) to show it in action.

And yes, I know that this would have been a 2-clear even without timing it just so. But the timing is the key. You can use this technique to create chains where you normally wouldn't get one, which can really put a hurting on your opponent.