I agree with fo3nix.
The drive in your laptop should have Windows on it, plus any programs you have installed.
The external drive should have your mp3 files, digital pictures, large video files like TV programs and films.
Make sure you MOVE the files from the C to the external drive, not just COPY them. If you COPY them they will be on both drives.
Make sure these files are also backed up to CD or DVD.
A hard drive has moving parts and can easily crash. If a hard disk crashes you will likely lose EVERYTHING on it, so ensure you have things backed up.