Trojan objects orbit 60° ahead (L4) or behind (L5) a more massive object. Both are in orbit around an even more massive central object. The best known example are the asteroids that orbit ahead or behind Jupiter around the Sun. Trojan objects do not orbit exactly at one of either Lagrange points, but do remain close to it, appearing to slowly orbit it.
The largest group of asteroids known to move around the Sun are those with the planet Jupiter. There are two groups of Jovian Trojans, one group on each side of Jupiter.