I was dating a girl years ago who was into it, and she used to talk about how people had moon signs too. Apparently mine is in Pisces.
Everyone has a Venus sign, Mars sign and so on. The moon sign is the most important along with the sun sign (star sign).
With a Pisces moon you are likely to have strong empathy, emotional sensitivity and compassion for others, especially anyone who is suffering, the disadvantaged, martyrs. Empathy may be so strong that you tend to absorb the emotions of other people, to the point where you may even take on their emotions and confuse them for your own, because boundaries are blurred in Pisces.
Strong intuition and gut feelings.
Need to do volunteer or charity work.
Vivid visualisation skills and imagination.
Tendency for daydreaming and escapism.
Aesthetic/artistic taste for the abstract (as opposed to more structured forms).