From Bulbapedia, the community-driven Pokémon encyclopedia.
Caroline (Japanese: ミツコ Mitsuko) is the mother of May and Max, and wife of Norman. Her Japanese seiyuu is 冬馬由美 Yumi Tōma and her English voice actresses are Megan Hollingshead (initial appearance) and Karen Neill (all other appearances). Her English name is a French feminine form of Charles, which means "man" in Germanic.
Caroline is May's biggest supporter, and traveled all the way to the Hoenn Grand Festival to support her daughter in her contests.
For a while, Caroline was mad at her husband because he wasn't spending enough time with her and too much time with Nurse Joy. As it turns out, Nurse Joy was helping Norman set up a fireworks display for his and Caroline's anniversary.
She is probably a Pokémon trainer, as in a flashback she is seen holding up a Poké Ball, but what she may train remains a mystery.