She also showed the book to the person next to her.
Literal
She [topic-は] book [object-を] neighbor [possessive-の] person [to-にも] showed gave.
隣の人にも見せてあげた — にも combines the recipient に with も ('also'). 見せてあげる uses the benefactive あげる to frame the showing as a kind gesture. 隣の人 ('the person next to her') is a natural way to refer to a nearby person.