。
She went to LA to study dance.
Literal
She [topic-は] dance [genitive-の] study [for-に] LA [to-へ] went.
ロス is the standard Japanese clipping of ロサンゼルス ('Los Angeles') — the same kind of two-mora abbreviation that gives スマホ for スマートフォン and コンビニ for コンビニエンスストア. The に on ダンスの勉強 marks purpose ('for the purpose of studying dance'), a productive frame with motion verbs: 買い物に行く ('go for shopping'), 食事に出かける ('go out for a meal'). The directional へ on ロス marks the goal of motion, slightly more atmospheric than に in this slot — に would also work and would feel a touch more pinpoint. From the postwar period onward, LA, New York, and London have been the iconic dance-study destinations for Japanese performers in jazz, ballet, and contemporary forms.