A backup is just another copy of the data you want to keep. It can be as little or as large as you make it.
There are programs out there that can perform automated backup's for you. They can be set to just backup files like your Documents, Pictures, Music etc; but they can also be configured to backup your entire hard drive (and thus be able to recover your computer completely to the time the backup was created. Documents again, Installed programs, everything as it is now). So it really depends on how much your backing up to how much space it takes.
If you are performing any kind of backup though, it would be wise the store the data on a separate hard drive or other media altogether. The idea is to recover your important files in the event of a complete hard drive failure.
Such a disk failure would potentially mean losing all your files, so I would consider a backup of some kind very important indeed.
Saying all that though, a backup could just mean having all your files, pictures etc burned to a cd or dvd. There! A backup! Of course, that backup would only be 'true' as to the time you created it. It would not take into account of any changes you have made since.