I think the Ribbons symbolize the party members' mutual friendship since they're all wearing one (you'll see a lot of Ribbons when all the characters lift Cloud to Bahamut). When Cloud goes to fight Kadaj near the end, he removes the sleeve and you'll see his Ribbon, so in a way that shows how he longer wants to be alone, but with his friends. The Ribbon is also there for Aeris' memory, as far as I know. Finally, Ribbon was the ultimate protective accessory in FFVII, protecting you from nearly all the status ailments.