I can't really tell you about the history of fly-fishing, but, surely, you can bring it up on Google with ease.
As for its advantage, I don't think it is either better or worse than other styles of fishing, it's just plain different.
If you want to try it without buying fly-fishing gear, you can do that. Lay your hands on a Bubble Bobber ( http://www.gofastandlight.com/Bungee-Bubble-Bobber-2-Pack/productinfo/FI-H-B-2PK/ ), and get the fun going. Good luck.
PS. Cabela's carries it too: http://www.cabelas.com/cabelas/en/templates/product/standard-item.jsp?_DARGS=/cabelas/en/common/catalog/item-link.jsp_A&_DAV=MainCatcat20166-cat20289&id=0019710111927a&navCount=1&podId=0019710&parentId=cat20289&masterpathid=&navAction=push&catalogCode=QX&rid=&parentType=index&indexId=cat601233&hasJS=true