yudpray,
The coat that you are thinking of is called a sportcoat because it was originally used in England for outdoor sports, mostly hunting. Sometimes these coats have leather patches at the shoulder to protect them against the wood of the gun-stock. Ofent they are reinforced with leather patches at the elbows to protect them against the brush, trees, etc. After WWI these coats became popular in America, mainly at universities and secondary schools, most likely because Americans associated them with the upper class and a superior British education. The patches have no real function today but style....unless of course you wear this coat when hunting.
What's is the function of the leather elbow patch on the kind of coat commonly worn by 80's actors? I often saw it in 70s or 80s movies. It's like the coat that Robert De Niro wore in Goodfellas.