An empire was a type of monarchy that was ruled by either an emperor or an empress. An empire was usually larger in scale then that of a kingdom, in fact an empire could have actually at times been made up of several kingdoms.
Other empires were even larger, some on an interplanetary and even interstellar scale, made up of several planets, moons, asteroids, planetoids etc.; often times including more than one solar system. Interplanetary empires included the likes of the Citadel Empire and Thanagarian Empire.
The United Planets was quite vast, with several solar systems that contained member worlds, however, it was not technically considered an empire, as the government, the capitol of which was Metropolis on Earth, was not a monarchy. Still, there were times when it may have been be considered as such due to its' size and power.