Q: How is the “Weak nuclear force” a force? What does it do?

The original question was: I keep reading on the internet about how it’s the electromagnetic force which causes positive and negative charges and their reactions, it is gravity which pulls all matter together, and it’s the strong nuclear force which pulls quarks together. What is it that the weak force does though? I have read that it “governs” radioactivity, but what does that mean? What is its purpose?

Physicist: The short answer is that the W and Z bosons (the Weak interaction carriers) really don’t “fit” anywhere else.  And, although it’s not the most important thing it does, the W and Z bosons do carry momentum, which is all that a force really has to do at the end of the day.
The big difference is that the other force carriers; photons, gluons, and (if they exist) gravitons, leave the involved particles alone (other than energy and momentum).  They’re very “clean” interactions.  While the Weak force can mediate interactions between particles without changing them (this is a result that helped point the way to the discovery of the “electroweak force”), it can also carry stuff with it, like charge.  By taking charge from one thing, and giving it to another, it’s changed the particles involved.  That last bit is important during “beta decay”, which is the type radioactive decay that the Weak force is involved in.

A muon and an electron neutrino exchange a W boson (carrying a negative charge, and some momentum), which changes the muon into a muon-neutrino and the electron-neutrino into an electron. This interaction is extremely rare. Far more common is muon decay, but that doesn't demonstrate the point.

Gluons can also cause the involved particles to change, specifically switching protons and neutrons.  However, if you start with one neutron and one proton, and you end with one neutron and one proton, what’s the difference?  The Weak force is the alchemist of the forces.