what is "ace trainer" mean?

Where are you seeing the term? In the main games, "ace trainers" are a class of npc opponent; the term "ace" (as an adjective) itself denotes the quality of comparative excellence in whatever profession/role/employment is next described, i.e., "Peyton Manning is the Broncos' ace quarterback."

If outside of the game, it's probably in some way derived from the main games.

It is an achievement for battling at gyms. The more you battle the higher your ace trainer achievement rank.

Oh, yeah, if you're asking about the term as found in this game, the medal (see more on the Medals page) is awarded after beating enough gyms. Its name like those of many of the medals is derived from a trainer class in the main games. (It's be neat if avatar customization derived from these medals and titles in the future.)