An external drive is a disk drive which may be plugged into a desktop or laptop using one of a number of types of cable, for example, USB v2.0, FireWire, or eSATA.
Your old machine might support one of those (eg a Mac may support FireWire) but odds are somewhat high against being able to plug in a drive - Windows 95 had poor support for USB, Windows 98 / 98 SE supported USB v1, but might need a plug-in card to offer USB 2, and if you are going to have to open the PC up, then taking the hard drive out and copying it entirely is perhaps an easier option.
You say your machine is old, so let's go back to basics... what system is it (Make, Model, Operating System) ?
Do you know how much disk space your photos (well, everything really, as the rest might be 2% of the 'used' portion of your machine) are using? It would be easy to point you to an external drive of say 500 GB but that could be significant 'overkill' for your needs.
It may be worth seeing if there's a local computer specialist, or small shop which will copy the hard drive for you. Once you can tell how much disk space is in use, it will be easier to judge whether a quote for copying the data will sound reasonable (assuming they include a brand new blank drive to hold your photos and other documents).
I mention someone else doing it for you because the older the machine, the less likely new (cheap) devices like external drives are to work with it, or work at a reasonable speed, if at all.
Have you already decided on buying a replacement system, or is this just feeling the need to copy what you already have "just in case" ?