A sun sign is the sign of the zodiac that the sun is moving through in the celestial sphere. The sign that the sun is passing through at the moment of your birth is your personal sun sign. It is this sign that is being referenced when you read your horoscope in the newspaper.
There are twelve signs of the zodiac. The sun moves through each of these for approximately thirty days before moving into the next in a cyclic pattern. The sun moves from one sign to another about the middle of the month, around the 20th, 21st or 22nd, this period is generally known as the cusp.