Royhobbs of Talking Chop provides a wonderful post about the experience of attending Turner Field.
Braves fans have long been the butt of attendance and fan jokes in general. The recurring joke every year during the division title run was that fans couldn't sell out a playoff game. Just to add: this is true because the Braves couldn't win a playoff game to save their souls, and I don't care who you are or where you come from, when you go to the playoffs every single year for over 10 years, you will get spoiled. It happens.
But another reason for a lack of a big game environment at the Ted is due to a lack of a reason to have one. As royhobbs points out in much detail, there is just nothing to do around the stadium prior to or after games. You travel to the stadium, you walk in and watch the game, and you go home. There are some tailgaters, but there aren't enough to cause a scene.
Of course, there are plenty more reasons for what seems like low attendance, all listed in that post and all being very credible and truthful. It's certainly worth a full read if you are one that scoffs at Atlanta residents for not filling the stadium on a nightly basis.