The weak nuclear force (or just the weak force, or weak interaction) acts inside of individual nucleons, which means that it is even shorter ranged than the strong force. It is the force that allows protons to turn into neutrons and vice versa through beta decay. This keeps the right balance of protons and neutrons in a nucleus. The weak force is very important in the nuclear fusion that happens in the sun. Nuclear fusion has also been created in laboratories, and that process requires the weak force to work too. See size of the universe for a list of visuals demonstrating how short ranged the weak force is.
Below is the Scishow's series on fundamental forces part 2, the weak force:
To learn about the other forces, please see the following pages: