noun
A short handwritten message or dedication written in a book, on a photograph, or similar item, often addressed to a specific person.
著者から本にため書きをいただいた。
I received a dedication in the book from the author.
卒業アルバムに友達がため書きを書いてくれた。
My friend wrote a dedication in my graduation album.
Compound of ため (for the benefit of) and 書き (writing). The exact historical derivation is uncertain, but the word literally means 'writing for someone's sake'.