Prepare for some info-tainment.
Why are we selling packs of 100 batteries today? Well, there are many ways to interpret this question. In one sense, we are selling 100 batteries because we think people will buy this many batteries at this price (wouldn't it be nice to have a stockpile?) But this isn't really the question. Why are we selling 100 batteries instead of 95 or 103? What makes the number 100 so special?
Nerds might have a fancy-sounding answer: We use a "base 10" number system, in which the position of a numeral reflects a power of 10. Since 100 is the second power of ten, it plays an important role in our counting system.
But even this explanation isn't totally satisfying. Sure, Americans use a base 10 system, but so did the Ancient Chinese, the Ancient Arabic, and pretty much every other civilization throughout history. Why didn't some cultures end up using base 8? Or base 23?
The answer is stupidly simple: We have 10 fingers. Do you remember how you learned to perform basic arithmetic? It was on your fingers. Our "digits" are the original base 10 counting system. Count up to 10, then start over.
OK, so why do we have 10 fingers? About 400 million years ago (notice how we rounded to a nice base-10 number?) the first tetrapods began evolving for life on land. As their fins evolved into feet over time, the foot bone morphology underwent several iterations. Some early land creatures had 12 toes, some had 8, and so on. Eventually, and probably almost purely by chance, the land-fish with 10 toes dominated and diversified.
So, to answer the original question, we are selling 100-packs of batteries because of a historical accident in the Palaeozoic.