An autograph is a person's signature and each one of us has a different way that we write. It is common for other people to want to collect the autograph of those they admire. It can be a political figure, a dancer, someone from the Olympics, a rock star, an athlete, and many other categories. Giving out autographs is often associated with the amount of fame a person has. Those original autographs can certainly be worth money later on though.
The autography can be on just about anything you can imagine. Paper and books are very common. Yet it is also possible for someone to place their autograph on your body or to put it on an article of clothing. For most people the memory of getting the autograph is worth much more than what is written on it. This means they got the autograph by meeting that person.
However, you will be able to find plenty of autographed materials online. They can be sports balls, pictures, clothes, and other objects. Many collectors want them even though they didn't get to meet the person. You do have to be very careful where you buy such autograph items from though. Not all of them are authentic. Even the certificate of authenticity that comes with them can be a clever copy.
The more generous a person is with their autograph though they less valuable they are. Yet most people want them for sentimental and personal value rather than retail value. Those autographs from people that have contributed to society or that have passed away though are often worth a great deal.
Some celebrities have chosen not to provide their autographs and that is an issue that doesn't sit well. They may come off as being unapproachable by their fans and this can result in them not supporting them any more. Many celebrities feel that they should be recognized for their talents though and not for their autograph.
You also have celebrities that don't like the idea of signing a picture for someone and later finding it on e-Bay. They feel taken advantage of an exploited. The personal decisions to offer autographs or not is up to the individual. It can be fun to gather autographs from those that haven't made it yet too. You never know when they may end up being the next big star.