She showed me her room.

Literal

She [topic-は] me [to-に] room [object-を] showed [for-me-くれた].

見せる ('to show') is the transitive partner of 見える ('be visible, can be seen') — a clean transitive/intransitive pair common in Japanese verb morphology. 見せてくれた combines 見せる with the benefactive くれる — 'showed me as a kindness.' Note the implicit possessor of 部屋: in context this is most likely her own room, though without further detail it could be any room she has access to. Japanese routinely leaves possessors unstated where context resolves them.