What is a moon sign?
Your moon sign is the zodiac sign the Moon occupied at the moment you were born. Where your sun sign is your conscious identity, your moon sign is your emotional, instinctive self — the private you. Because the Moon moves fast, changing sign every ~2.5 days, two people born days apart can have very different moon signs.
Your Big Three
Your moon sign is one third of your Big Three — Sun, Moon and Rising. The Sun is who you are, the Moon is how you feel, the Rising is how you come across. Want the whole picture? Get your full birth chart with every planet, house and aspect.