Nirn has two moons which dominate the sky. The larger red moon is known as Masser and the smaller silver moon is known as Secunda. The moons are not celestial bodies as we would understand them, but rather they are the remains of Lorkhan and we perceive the results of his death. (I think I have that straight…)
In ESO the new moons are linked to vampires (full guide) and the full moon to werewolves (full guide). NPCs should spawn on the relevant moon phase to infect you with either condition, however, it has been reported (forums / reddit for e.g.) that spawns are now random… I recommend this addon to keep track of the moon cycle.
any excuse for night sky screenshots: