Do "Backups" appear on your Mac's hard drive, on the external drive or on both of them? It's normal that you see "Backups" on the external drive, but also it's normal to see "Backups" on the Mac's hard drive if you are using OS X Mountain Lion. That's because OS X creates local snapshots on the hard drive > http://pondini.org/TM/30.html
If you want, you can delete or turn them off, but they are automatically deleted when the hard drive gets full, so you don't have to worry about that. Apart from that, if the external drive where you make Time Machine backups gets full, Time Machine will start automatically deleting old backups