Due to a phenomenon called the precession of the equinoxes, the position of the stars slowly shifts over time. Every 72 years, the spring equinox moves backward by one degree through the zodiac.
This means that over approximately 26,000 years, the equinoxes make a complete cycle through all twelve signs. This is why the "Age of Aquarius" is discussed - we're transitioning from the Age of Pisces.
However, Western astrology uses a tropical zodiac tied to seasons, not star positions, so your birth sign remains the same regardless of precession!