Capillary action means either of two things:
Capillary action is a result of the surface tension of liquids.
One example of capillary action is that inside a drinking straw left in a cup of water. What holds the water together and to the straw is a little stronger than gravity, so the water will rise inside the straw a little higher than the rest of the water.
Another example is putting a sponge in a puddle of water. The little bubbles in the sponge work like a bunch of little straws all stuck together. When you dip the sponge in water, the water goes a little bit into the holes, and then the bubbles that are inside the sponge can pull on the water that they touch.