Someone who's spirited is lively or enthusiastic. It can be challenging to babysit a bunch of spirited four-year-olds, but it's also entertaining.
You can also call a spirited person energetic, animated, or spunky. Spirited people are often determined, too, like a spirited activist for animal rights or a spirited defender of free school lunches. Long ago, this adjective was also used to mean "possessed by a spirit or ghost." Today's sense of spirited comes from the original meaning of the verb spirit, "to make more active."