。
She really wanted a doll for Christmas.
Literal
She [topic-は] Christmas-present [as-に] doll [object-を] very wanting-was.
ほしがる is the third-person desire verb. Where first-person speakers use ほしい directly ('I want a doll' = 人形がほしい), Japanese requires extra grammar for talking about other people's desires — you can't observe their inner state directly, so you describe its outward signs with the suffix ~がる ('show signs of'). ほしがっていた is the past continuous: 'was showing signs of wanting,' i.e., 'really wanted (over a stretch of time).' Note the particle shift too — first-person ほしい takes が, but third-person ほしがる takes を because it's a transitive verb of behavior.