If you sign your name on something, you autograph it. You have to autograph a check before it can be cashed.
An autograph is a signature. Famous people are asked for their autographs all the time, but you might be surprised and flattered if a little girl asked for yours after you played Dorothy in your community theater production of "The Wizard of Oz." An original manuscript or musical composition written in the handwriting of the author or composer is also called an autograph. In 1938, the Museum of Modern Art displayed an autograph of Mark Twain's "Tom Sawyer."