I use it for sharing files that are too large to easily email--like high-res video & multiple large photos. You can share a file or folder with anyone else who has Dropbox, all you need is their email.
It's a good way to handle a situation where multiple people work on a project. You still can't have the same file open at the same time, or one version will over-write the other, but it's very handy.
It's also a good place to backup files, since you can easily restore them to any computer.
For handling large files or backups, you will need the paid version, which is $99/yr for a terabyte.
You can also automatically sync a file that you use on different devices.
It's worth $99/yr to me, for sure.