I thought that it represented his family like a coat of arms does. Also, it is the only one of its kind, and the fact that Link uses it shows its importantce to him. Being the only Hylian in Ordon, it might also be used to mark that difference. Of course, it could just be decoration, but I don't really think it was designed just as that. I liked how we did not know anything about his family. But I wish we learned more about them throughout the game. Then again, they may tell us in SS if it turns out to be TPs sequel. We can only hope. But the banner may always be a mystery, but I think it shows Link's history before his heroic exploits.