An association copy has a meaningful link between the copy itself and the author or the book's story: a copy inscribed to a friend, a fellow writer or a person who appears in the book, or a copy that belonged to someone important to the author.
How to spot it
The usual evidence is an inscription that names the recipient, a bookplate or ownership signature of a notable person, or annotations. The link must be documented: a name in the book is only an association if the person can be identified and their connection to the author shown, through letters, biography or provenance records.
What it does to value
Association copies are among the most valuable copies of any book, often worth far more than a plain signed copy. The closer and more significant the link, the higher the value: a copy inscribed to the author's spouse or to the real person behind a character can be worth many times a copy signed for a stranger at a book signing.
Read signed and inscribed books for the difference between a signature, an inscription and an association, and how much is my book worth for what moves value most.