An autograph show is an event where the public, mostly autograph collectors or fans of an attending celebrity, gather to collect autographs from someone famous who attends to meet fans and sign items
Fans at an autograph show
Puerto Rican singer Melina Leon at an autograph signing
An autograph is a person's own handwriting or signature. The word autograph comes from Ancient Greek, and can mean more specifically:
"B-A-C-H is beginning and end of all music", signed autograph document by Max Reger (dated 7 May 1912)
Picture of German yodeler Franzl Lang, autograph (likely for a fan's collection) at bottom.