It's a condition when a pregnancy starts but something called a "hydatidiform" mole" develops. There can be a partial molar pregnancy, which includes some development of fetal tissue; or there can a complete molar pregnancy, in which there is no fetal tissue - only the "mass" (which is the mole).
The mole starts to form when something goes wrong at the time of fertilization. Instead of developing tissue for a normal placenta, the pregnancy includes the mole instead of that normal placenta tissue.
The condition is not common. Most of the time the mole is not cancerous. It can be in a minority of instances. D&C is a common treatment, which clears out the contents of the uterus. Hysterectomy is occasionally required.