The unallocated space on a hard drive, generally refers to a portiton of the hard drive that needs to have a partition created and formatted before you can use it to store data.
If you mean free space available, that's entirely different.
To backup to your hard drive, you would need a second partition or hard drive. A second drive internal or external is better, in the event of systems failure your data would be safe.
Burning your data files to cd/dvd is more secure and the prefered option for important data.
Windows has builtin backup tools, read your help files for instructions.