I think DrMoriarity has it right, except to say that many external hard drives come with backup utilities on a hidden partition on the hard drive.
Some of these utilities allow you to encrypt the data, but that's usually a manual operation.
Other utilities allow for automated incremental backups.
I think some will allow you to specify an automatic backup when shutting down, but I'm not certain of this.
One other thing you should consider is the security of your information.
Some backup solutions have encryption facilities hard wired into their motherboards and allow for "transparent" encryption, i.e. once you're logged on to your computer, you can simply backup data without worrying about the encryption.
Like most things you have too research what's right for you, but if data security and retention is your goal, you need to look at this.
The reason is that while the data on your computer is protected to some degree by your login password, the data on an external hard drive is not usually so protected.
Which brings me to the hard drive itself.
I have spoken to a data retrieval company and they suggest discrete encrypted containiners as opposed to whole disk encryption.
One reason for this is that encrypting the whole disc can in theory cause problems if some data becomes corrupted, because of the way encryption writes data back to the disk.
The other reason is that the procedure to recover from a corrupted encryption header is difficult enough without having to do so before you can access the HD - a lot of planning is needed to prepare for this.
Having the data encrypted in pockets on the hard drive means it is protected within the operating system but the entire system is otherwise unchanged.
This leaves the swap file as a source of unencrypted data should the laptop be stolen.
However whole disk encryption deals with this, taking the risks above into account.
HTH
ONQ.