In Spanish, masa means "dough", but in Mexico that's generally assumed to mean corn dough. Masa harina is "dough flour", made from dried ground corn dough.
Masa is made from hominy: dried corn (maize or sweetcorn) kernels that have been boiled in powdered lime (calcium oxide), left to soak overnight, and ground. Mixed with a little water, the resulting dough can be flattened into tortillas or wrapped in a corn husk and steamed to yield tamales.
Masa harina is masa which has been dried and ground into a flour, and it's the only way those of us who don't live in or near Mexico are going to get masa. Instructions for using masa harina to make corn tortillas are here, and if all you've ever had are those crisp yellow cardboard taco shells from the supermarket, you'll be amazed how much better these ones are. But the real thrill is going to Mexico and having fresh handmade tortillas from masa.
Store masa harina tightly sealed in the fridge and use it within a year; it doesn't taste very nice once it goes stale.