。
She got the book for him.
Literal
She [topic-は] him [to-に] book [object-を] took-and-gave.
~てあげる is the benefactive auxiliary 'do for someone' — here attached to 取る ('take, get, fetch') to mean 'fetch (it) for him.' あげる (vs. やる) is the neutral/elevating form, appropriate when the recipient is socially equal-or-elevated, or just neutrally framed. に on 彼 marks the recipient. The same action with やる (取ってやった) would imply slightly closer/more casual relations or condescension; with さしあげる, formality.