What does "AA" stand for on a battery?

The letters on a battery give the size, in height and width, of the battery. AA means “50.5mm x 14.5mm.” The later the letter the larger the battery. "D" is larger than "C", etc. "A" is larger than "AA" is larger than "AAA".

As well as the recommended size code definitions there are also ten modifying suffix letters that can be added to the end of the specific size code.

These run from A to L (omitting F and I) and depending on the largest dimension of the battery can either signify 0.0 – 0.9 mm maximum dimensions or 0.00 – 0.09 mm maximum dimensions with A being 0.0 or 0.00 and L being 0.9 or 0.09.

https://en.wikipedia.org/wiki/Battery_nomenclature

The system of classifying batteries by size in letters is one going back at least to the 1960s. Originally there were four sizes - A through D - in ascending order. In the 1980s smaller batteries started to become easier to make and less expensive to buy, and when sizes smaller than A required classification, AAs were invented, followed by the AAA.

I should note that this is all from memory; I wouldn't know where to look for a source reference site on the matter.