A star system is a single or pair of stars that orbit each other and all the planets, asteroids and other astronomical features that orbit it or are within a reasonable distance. However, since the gap between each star is so huge, features are simply grouped with the closest star, so there is no set distance. One famous star system would be our own, the Solar System.
In Spore, you cannot traverse your own star system until you have built a UFO. Will Wright has suggested that most star systems have between four and five planets or other celestial bodies, although more may be possible. While star systems with multiple stars are possible, they are classified as Galactic Objects and are not all that common (though they appear to be in greater numbers the closer you get to the center of the galaxy)
Star system view
Viewing the star system from the UFO, you will be able to see the star in the center, and the planets orbiting around the outside. By moving the mouse over the planets, you can scan them to see what types of life they have on them, what atmosphere etc. This scanner will also show sentient life and possibly whether or not there is an Artifact on it. Planets especially close to their home suns sometimes have an elliptic orbit.