Capillary action means either of two things:

1. When liquid moves through thin tubes.
2. When liquid moves through something that is full of little holes (like a sponge).

Capillary action is a result of the surface tension of liquids.

An example of capillary action is what happens inside a drinking straw left in a cup of water. The force of adhesion which 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.