Your sun sign is the zodiac sign the Sun occupied at birth. Your Moon sign is where the Moon was. Western astrology highlights the sun sign, while Vedic astrology often starts with the Moon.
Why the Moon?
The Moon moves quickly and reflects mood, habit and emotional response. Because it changes sign roughly every two and a half days, your Moon sign is more personal than your sun sign.
Which should you read?
Read both. The sun sign shows the core self and direction; the Moon sign shows inner reactions. If you know your birth time, your ascendant adds a third layer.