From Diablo Wiki
To quote an official FAQ on the matter:
A: Think you're better than all of your friends? Your banner will prove it. The banner system will be a visual representation of the achievements players earn across all of their Diablo III characters on their Battle.net account. A player’s banner will have multiple components that can be earned through various modes of gameplay. Completing different parts of the game at different difficulty levels, defeating bosses, earning achievements in PvP, and earning various other achievements will unlock ways for players to customize their banner and show off their progress in the game.
The tip of the banner will be adorned with menacing-looking objects (as seen in the image at right) for those who choose to participate in Arena battles. The small strips of cloth hanging from the golden skulls represent how many achievements the player has earned (on that character), and the tabard itself seems to "grow" as the character is leveled. Hardcore players are rewarded with the unique-to-Diablo-series "bones that bleed" decoration along with a longsword lodged into the pile for good measure.
Customizing the Banner
Several different aspects of the banner can be customized, accessed by clicking on the banner itself in the character select screen. The first being the banner itself; the general shape of the banner can be chosen by the player as well as the pattern adorning it. The player can also choose a sigil and an accent to go under the sigil, in addition to the position of the sigil. After that, the player may then choose the dye colors of the banner, pattern and sigil to match their liking.
If a player doesn't wish to sit down and take the time to customize the banner manually, there are options to have a random banner generated, or an auto option that will automatically generate a random banner every second.
The banner has a function in the game, other than simply looking neat. The player may place their banner on the ground (default hotkey for this is "G"), and it will show up in the nearest town. The friend or party member may then click on the banner in order to teleport to that player.
In the beta players of any level can use the banner to teleport instantly to another player so in effect a level 1 player could teleport to a much higher level area, intentionally or not.
Banner customisation video