Stewing with Apple Cider Vinegar
An acid in a stew serves much the same purpose it would in a marinade. It aids in the tenderizing (typical 'stew meat' is cut from inferior cuts of the beef and can be tough) and balances the flavors. (As such I would disagree with @lspare about adding it "at the end", it needs time to do it's work) 

Browning is a separate issue. Browning is the result of the Maillard reaction and should occur when stew meat is seared prior to being incorporated into the stew. In a stew the 'cooking temperature' is never above 212°F (100°C) and this will not 'brown' the meat.