In order to clear fireflies, you need to get all of them to stage 3 (the excited and flapping stage) at once. Each time you make an adjacent match or hit a firefly with a power tile (lily, sunflower, stripe, etc), it will progress 1 stage.
Be careful, though, because if you hit a firefly when it's at stage 3, it drops back to stage 1.
In general, you want to work from bottom to top for the fireflies. It's easy to accidentally hit the fireflies at the top of the board with cascades when you make a match near the bottom of the board, so focus on the highest fireflies last.
Think of it like a swarm: the fireflies stick together. When they are all brightly lit and flapping, they will fly away together.
Here is a video that shows this mechanic in action: Fireflies Level
It may also be useful to replay the tutorial level (157), where the objective is easier to meet. Playing the level without the tutorial will let you see the mechanic in a relaxed environment.