west is the manufacturer/distributor of an epoxy resin, the term "system refers to the range of products available as addatives, allowing the resin to be mixed with other things like microfibres for "thickening" or microbaloons for filling/fairing.
Years ago, a technique was developed for building boats using carefully dried wood which was then saturated in epoxy resin. This new technique produced a strong and durable construction. The technique became known as the Wood Epoxy Saturation Technique, leading to the acronym WEST, which a company called Gougeon Brothers adopted as a brand name for their resin. It's developed over the years as lightweight microballoon fillers, etc, have become available - leading to more versatile uses of epoxy on boats. So it's both a brand and an acronym for the original technique.
West System products are good quality, but there are many good quality alternatives, both branded and generic. International Epiglass is a commonly-found alternative brand.