Your “Battletag,” simply put, is your name on Battle.net. Not your Real ID, which is a separate ,”optional layer of identity” that enables additional features between online friends who choose to share their real names, but just a convenient handle or alias—a “nick,” as we used to call them on IRC. Battletags don't have to be unique (Blizzard tacks a number onto the end of each to differentiate them), and, aside from the limits imposed by Blizzard's naming policy, you can make it whatever you want.
What you can't do (or at least haven't been able to do until now) is change your Battletag more than once. Blizzard's standing policy gave every user one free Battletag change, but after that you were stuck. So if you one day came to regret your decision to call yourself XxMrSwagNutz420xX, well, that was just too bad. But that policy has how changed, and you may now change your Battletag as often as you like—as long as you're willing to pay for it.
The Battletag Name Change is now available for $10 as a Battle.net Game Service. You can buy as many as you want, meaning that you can finally indulge your impulsive, mercurial love of nominative determinism in the online world, and it won't have any effect on your friends list or other such online paraphernalia. And as was previously the case, the first change remains free. Blizzard didn't say why it made the change—as far as I can tell, it didn't even say it had made the change at all, it was just noticed by some sharp-eyed Redditors—but given how long people have been asking for this option, it's nice that it's finally happened.
Seeing as you've made it this far, if you're looking for inspirations for your next Battletag, I highly recommend following the wonderful @battlenet_txt Twitter account to see some astonishing names which made it through Blizzard's filter.