Dropping the banner does nothing mechanical in-game. I do not know of a quote from Blizzard explicitly saying this, but there is reinforcing evidence:
1) From the D3 FAQ:
What is the banner and sigil?
The banner is a customizable flag that shows off your achievements and progression when playing Diablo III. Your banner is displayed within the chat interface, in multiplayer games, and on the official Diablo III website. There are many individually customizable pieces of the banner, each of which represents a different section of the game...
This says that the banner is primarily a means to display your progress through the game and your accomplishments. Early in beta there were even plans for more advanced banner progress to show off your status.
There is also a D3 blog post that indicates they intend the banner to be just a means of identifying players, and you can click a banner in town to teleport to that player.
2) Forum threads: there is discussion of this on the official forums, and the concensus is that banner dropping doesn't "do" anything (but lots of people wish it did!)
3) Documentation: If the banner drop feature did something mechanically, Blizzard would document it, have 4 different tooltip popups pointing to it, mention it in their game guide, blog about it, post it to Twitter, and have airplanes fly around pulling banners mentioning it. My point is that Blizzard is very big on helping new players understand the game's features, and there are no signs that the banner does anything.
4) Other games: Finally, if the banner was for marking mobs or targets, I suspect they would follow the lead of WoW, which has a very clear and specific feature for marking raid targets. Blizzard loves to re-use features, so they would probably do something similar.