Why does restoring my iphone from a backup use up so many gigabytes?

I have an iphone 5 and I'm trying to restore my phone from last backup. Unfortunately, the back up is cancelled about 30 minutes in because my hard disk runs out of space. I have 10 gigs left so there should be any problem with that. I went to mobilesync folder and then to the backup folder and there's one folder there. Once you click on that folder there are thousands of files in that folder that have several modified dates on them. Basically can I just delete the old dated files?

Restoring, per definition, does not use any space on your HDD, only on the iPhone.
Or more precisely, if it does, somebody screwed up sonically. I think Apple did; the restore should delete the data from the phone before restoring. (Are you using a third party tool?)

Somehow there seem to be data on the phone (they come in 8 and 15 gigabyte, not 10); you should delete them manually and then restore.

Hope that helps.