Colossus was the world's first programmable (to a limited extent) digital electronic computer.
It was built by the British Post Office Research Station at Dollis Hill, by Thomas Flowers and crew to a design by Max Newman and associates of Bletchley Park.
It was primarily designed for cryptanalysis in an attempt to break one of the cyphers used by the German military for its most secure strategic communications during WWII.
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.