Fab is simply short for fabricate or fabrication which is a term commonly used in all manner of manufacturing including circuitboards. An external party that provides manufacturing is often referred to as a 'fabrication partner' or 'fabricator', shortened to 'fab'.

https://en.wiktionary.org/wiki/fab#Noun https://en.wiktionary.org/wiki/fab_lab#English https://en.wiktionary.org/wiki/fabricator#English and if you really want to understand the English culture don't miss https://en.wikipedia.org/wiki/Absolutely_Fabulous ;)