It's not trying to back them up wirelessly, its backing things up internally.
If you have TM 'on' but no TM disk connected, your MBP will make 'local snapshots' - temporary TM backups that are saved on your internal HD. This was a new feature added in Lion which allows you to use TM even when TM is not connected - or at least, to go back to undo changes that you've made even while TM is disconnected.
You can turn it off if you want, but it's quite a handy feature if you're out on the road with your MBP and only connect to TM when you get home at night or whatever.
To disable local snapshots, connect TM first and complete a normal backup.
Then open Terminal and type
sudo tmutil disablelocal
Press 'return' and enter your admin password.
If you want to turn them back on again, replace 'disablelocal' with 'enablelocal'.
I just recently upgraded to Lion, so that is why I was not aware of this feature.
1. How does TM make local snapshots and store all of that on the drive of the Mac? How is there space for it?
2. Are you saying that I can restore a file that gets accidently deleted without even having the external drive connected?