To an astrologer, the Sun, Moon and Planets represent energies in your life: for example, Mercury represents communication skills, whilst Venus represents your aesthetic sense, your love of beauty and the more romantic side of your personality. By understanding these energies, and knowing how they are moving through your chart, astrologers can show people how they can get into better touch with themselves, and with their lives.
The Sun and Moon are not, of course, planets. However, they are treated as such in astrology. This is because astrology has the Earth at its focus, and is interested in the positions of astronomical bodies with respect to the Earth.
The addition of the asteroids is a new technique. The asteroids are a group of smaller bodies which lie between the orbits of Mars and Jupiter. Some ancient myths hold that they are the remains of a small planet which exploded or collided with another body. However, many astronomers believe that they are debris which remained after the other planets were formed.
Because there are so many asteroids, it is difficult to know which ones might be significant astrologically. In practice, the only four which are used are Ceres, Pallas, Vesta and Juno. These are believed to be related to the mythology of the goddesses after which they were originally named. Since they are related to goddesses, rather than gods, they express feminine aspects of personality. Some feminists astrologers believe that the asteroids are particularly relevant to present-day society, because they represent archetypes of women who are emotionally strong and independent.