She launched into playing the piano with enthusiasm.
Literal
She [topic-は] [eagerly-熱心に] piano [object-を] [started-playing-ひきだした].
ひきだす is a compound verb: 弾く ('play [an instrument]') + 出す ('emerge, come out'). The ~だす auxiliary on action verbs gives 'suddenly start, burst into ~ing' — a sharp transition into the action. Common variants: 笑い出す ('burst out laughing'), 走り出す ('start running').