。
She's eager to learn new things.
Literal
She [topic-は] new things [object-を] is-showing-desire-to-learn.
学びたがる combines 学ぶ ('to learn') + たがる (third-person desire). The ~ている marks this as an observable, ongoing state — her eagerness is visible to the speaker. こと here is used as a generic noun meaning 'things,' making 新しいこと = 'new things.'