It is basically giving you a choice between an Master Boot Record partitioning format, which is the current standard and bootable and recognizable from a standard BIOS driven Motherboard...

OR you can partition it in the newfangled GUID Partition Table partitioning format which is supposedly newer and better. It was started by Intel for their Itanium processor wich uses whats called an Extensible Firmware Interface, or EFI as opposed to a BIOS.

Since this is an external drive, and a backup drive, and you aren't running a server, and you probably aren't a glutton for punishment when it comes to being the first to try something new, then the MBR is the one you want.

I believe you can plug an MBR drive into an EFI architecture and it should still function, but if you plug a GPT drive into a BIOS architecture it may not support GPT, and depending on how badly it doesn't support it, your data might be inaccessible or worse written over. I haven't dealt that much with this, so if someone knows more, by all means post.

As for your situation, I would recommend just plain old MBR.