Check wikipedia. The term started from an Oxford Rowing club who created striped jackets for themselves in the early 19th century. The rowers were referred to as blazers because of the big striped blaze across their jacket. THen there is the other defintion of striped jackets on the HMS Blazer a few years later.
These days a blazer is a slightly casual, and often quite outlandishly coloured jacket worn by Sailers, Rowers, Cricketers, tennis players etc, plus the military and schools. Logos and shiny buttons are common.
Not common in Golf however, at least not in the UK. Lower end clubs may have them, but generally regarded as terribly naff at the top end. The president may have one for special occiasions, but generally a striped club tie and nice tweed jacket is considered more appropriate.