A natal astrological chart is derived from your date of birth plus the time and place you were born. It is essentially a map of where the constellations were in the sky at that precise time. Your chart can reveal where the known planets were placed both above and below the horizon. Your sun sign simply reveals with which constellation the sun was associated when you were born. Someone with an Aries sun sign was born when the sun was close to the Aries constellation. In astrology, your sun sign reveals in a very broad sense that you will share some basic life motivations and characteristics as another Aries sun sign person. As mentioned prior, your Sun sign is less about who you are, but more about who you are to become in this lifetime.
This quick explanation of sun sign astrology is merely a jumping off point, however. Remember, there are other planets and heavenly bodies, too, that were also present in the sky on the day you were born and each of them has a unique influence on you. This mix of planetary positions and their influences will show you how you are not just an Aries like all other Aries, but instead you are a blend of all of those planetary influences on the day you were born as are they. Your natal astrological chart is a snapshot of the sky at your moment of birth and will show you what you came into the world with and how you will grow in your time on earth.
In addition, the sky is also divided into 12 sections, or "houses," into which the planets are placed. Each house governs a particular area of your life, ie., the 10th house is about career and status while the 5th house is about romance, children, creativity and gambling. Where the planet falls in respect to the houses shows in which area their influence is acting. Obviously, the planets have continued to move since the day you were born and that movement upon your natal planets and in your natal house positions defines how you will continue to grown and develop under their influence.