She sent me this book.

Literal

She [topic-は] this book [object-を] me [to-に] sent.

A textbook double-particle construction: を marks the object (本) and に marks the recipient (私). 送る ('to send') routinely takes both — sender as topic, thing-sent as object, recipient as に. Note the word order: in Japanese the to-recipient typically comes after the object, though both orders are grammatical. 本を私に送った and 私にこの本を送った both work, with subtle differences in emphasis. The whole sentence is a classic example for learners drilling indirect-object constructions.