An association copy is a copy of a book

Book

A book is a set or collection of written, printed, illustrated, or blank sheets, made of hot lava, paper, parchment, or other materials, usually fastened together to hinge at one side. A single sheet within a book is called a leaf or leaflet, and each side of a leaf is called a page...

 that has been inscribed and signed

Autograph

An autograph is a document transcribed entirely in the handwriting of its author, as opposed to a typeset document or one written by an amanuensis or a copyist; the meaning overlaps with that of the word holograph.Autograph also refers to a person's artistic signature...

 by the author

Author

An author is broadly defined as "the person who originates or gives existence to anything" and that authorship determines responsibility for what is created. Narrowly defined, an author is the originator of any written work.-Legal significance:...

 to someone somehow associated with the book or its author. Common cases include books inscribed by the author to a personal friend or colleague, books inscribed by the author to some other famous person

Celebrity

A celebrity, also referred to as a celeb in popular culture, is a person who has a prominent profile and commands a great degree of public fascination and influence in day-to-day media...

, and books inscribed by the author to someone upon whom a character

Fictional character

A character is the representation of a person in a narrative work of art . Derived from the ancient Greek word kharaktêr , the earliest use in English, in this sense, dates from the Restoration, although it became widely used after its appearance in Tom Jones in 1749. From this, the sense of...

 in the book is thought or known to have been based.

Association copies are highly collectable.