This is how a recent game of guess-my-sign went down for me: "You must be a Scorpio. No, wait — Virgo? Pisces? That's it. Definitely a Pisces." My guesser was close — my sun sign may be Capricorn, but my rising sign is Pisces (the sign that was rising over the horizon at the moment I was born).
If you've never had your birth chart drawn up, you probably don't know what your rising (or ascendant) sign is. Along with your sun sign and your moon sign, it's one of the "three legs" of your chart — it's part of the foundation of your personality, so it's important to keep your rising sign in mind when you read your horoscope.
Where your moon sign indicates the inner you, your rising sign can tell you more about your "outer" self. In other words, your rising sign is what people first see when they meet you. Think of it as your "first impression" sign.