What does dropping your banner do?

When I press G on the keyboard, my character summons down my banner on the spot. It hangs around for a few seconds, then disappears.

What is the purpose of this?

Solution 1:

"Dropping your banner" with G is an emote that serves no immediate function.¹

At best, it's a customizable emote that shows off your swag—your in-game achievements convert to banner adornments. You can also change the banner's color, sigil, and shape to reflect your taste.

Dropping the banner will create a marker on the map for party members (orange arrow, turns to pulsing circle when close)

Solution 2:

It's just a mechanism to show off your Achievements. Various achievements unlock certain things for your banner, and by pressing G you can throw it down and show everyone that you've got all classes to Level 13 in the beta (for example).

Source: http://us.battle.net/d3/en/game/whats-new under "Achievements"

ACHIEVEMENTS

You'll be able to show off your achievements with a battle standard, a banner visible to all players on Battle.net that will be a visual representation of your accomplishments in Diablo III. And you should expect even more ‘endgame' additions to come - ones that'll let you pursue unique goals and achieve more glory in the world of Sanctuary than ever before.

Solution 3:

It also marks the point on the map while the banner is dropped, useful to point out a location to other players - eg elite enemy, resplendid chest etc