Banners are used to convey information about players, they show you current difficulty level, your achievement tally, whether your a hardcore or a softcore player and your pvp rank. As you can see in the screenshot the banners are placed around the waypoint in New Tristram so other players can see how rediciously  cool you really are.

 

You can customize the banner with the Diablo III Banner System , this allows you to style, color and symbolize it. There are tons of options available, check out the preview for a detailed look at the banner designer.

 

You can unlock further banner decals by completing achievements so you can show off your progress.