It may be one example of a method that was used by an early investigator for whatever reason, then became fixed as it was copied by everyone afterwards because it worked well, and nobody ever bothered to try to improve upon it. Once it was ensconced in Maniatis, it became standard procedure.
This Wikipedia article (https://en.wikipedia.org/wiki/TAE_buffer) points out that using acetate as the anion has an advantage over borate (as in TBE) is that acetate doesn't inhibit enzymes that might be used on the DNA extracted from the gel, as borate does.
Someone will hopefully give a more complete answer, but the short answer is "adjusts the final pH of the Tris buffer". There are two general forms of TRIS - base (trizma), and acetate (HCl). Historically we would make solutions of Tris-base and Tris-HCl and mix to get the right pH for the final Tris solution. I don't think many still do that. But the historical TAE buffer used Tris-acetate, plus glacial acetic acid to adjust the pH. TRIS provides the buffering power, and EDTA, historically, was most likely in there to "stabilze" the DNA, by inhibiting nucleases by chelating Mg++. DNA is much more pure now and most of the historical issues are not really issues anymore, but TAE is still a great running buffer for agarose gels.
It may be one example of a method that was used by an early investigator for whatever reason, then became fixed as it was copied by everyone afterwards because it worked well, and nobody ever bothered to try to improve upon it. Once it was ensconced in Maniatis, it became standard procedure.
This Wikipedia article (https://en.wikipedia.org/wiki/TAE_buffer) points out that using acetate as the anion has an advantage over borate (as in TBE) is that acetate doesn't inhibit enzymes that might be used on the DNA extracted from the gel, as borate does.
"As you know it, TAE buffer contains tris, edta and acetic acid, the acid reacts with water tremendously because it is concentrated. The reactivity with water causes the solution to change the pH, as we know that solutions use is based on their pH in most cases. So, acetic acid purpose is to allow dissolving of salts/edta by pulling down acidity in solution and thus tris functions to reduce the state brought by acid."