Retrocomputing is the use of computer hardware generally judged obsolete. One example would be to use a Cambridge Z88 or a Tandy Model 100 to do your work instead of the latest Pentium, multimedia laptop. Some people have no use for or can't afford a modern computer and choose to work on older computers instead. If you use the computer only do do word processing perhaps you are satisfied with an Amstrad PCW.
A related subject is retrogaming and abandonware. It's a bit different and seems to be mostly based on wanting games based on good gameplay instead of effects.