Capillary action is the ability of a fluid to flow in a very small narrow space and against gravity (as it flows upwards).
The movement of a liquid in a narrow space along the surface of a solid body is due to molecular attraction.
What is molecular attraction?
Molecular attraction is the ability of the molecules of a liquid (such as solder) to attract the molecules of a solid (such as a copper pipe).
During soldering, the solder flows between the copper surfaces and provides a secure connection. This happens without help and in spite of the external force of gravity.