If you own the copyright on something, you get to control who can:
- Copy the work. This means any kinds of copies including digital/online copies too.
- Create derivative work or collect money from derivative work. This means that if anyone wants to create anything based on your work, they have to get your permission and give you money.
- Distribute copies of the work. This includes distributing hard copies (like a paper copy), digital copies, and basically any copies in any format.
- Perform the work in public, or get royalties if someone else does. If you wrote a play and a theater group wanted to perform it, they would have to pay you royalties.
- Display the work in public. Say you're really into photography and even sold some pieces at a gallery. It's OK if the person who bought the work displayed it in a private area, like her home. She could not, however, display the photograph in a public space, like a museum, without your permission.
You know that Jeopardy jingle that plays during final jeopardy? Merv Griffin would get paid a royalty every time it's played.
Usually the creator of the work owns the copyright, but not always. For more, see Nolo's "Copyright Ownership and Rights" or 17 USC 106.