Edit: Because I've gotten a lot of PMs about it, the podcast is by Mike Duncan. It's a full, comprehensive history of Rome, and if you're not a fan of hours long podcasts, the episodes are fairly short.
I'm currently listening to the History of Rome podcast (if you haven't listened to it yet, do it right now), and I'm still in the Roman republic era, yet Rome is shown to have fielded massive armies. The typical army was 40-80 thousand (depending on how many consuls were commanding an army) and sometimes armies numbering in the hundreds of thousands were raised. And this didn't just include Rome. There are multiple times where outside powers engaged Rome with armies just as massive, such as the Gauls and I believe Carthage, who engaged with massive armies numbering up to 100 thousand.
Now because I know this subreddit prefers specific times, for a point of comparison I'll look at England during the Hundred Years' War era, while searching for an answer here, I found a comment saying the English armies were rarely higher than 15 thousand. I'm on mobile so I'm unable to link the comment at the moment.
So my question: What the hell happened? Comparing the middle Republic era of Rome (not even the height of their power), to one of the more well known series of conflicts of the late medieval era, and Roman armies, as well as a few other ancient armies, were way more massive. Though if there are any experts on other times and places in medieval Europe, I'll take answer on that as well.
Firstly, keep in mind that the ancient armies you are describing were fielded by what were essentially ancient superpowers. At the time of the Punic Wars, the Carthaginians held an empire that controlled the western Mediterranean, spanning much of North Africa and Spain. Similarly, when you look at the various Persian Empires, they controlled vast territories and had a large population base to draw upon (consider Thermopylae, where the smaller Greece was only able to assemble a few thousand men against the hundred thousand of Persia). The size of the ancient powers' armies was larger than those of medieval kingdoms in part because the ancient powers were simply larger than medieval kingdoms.
With the Gauls and other European barbarians that the Romans encountered, often the Romans were encountering an entire society of people who were living there (Gaul) or an entire society that had picked up and migrated (Cimbri, Teutones). The size of their armies gets blurred a bit there, since numbers may include civilians as well as soldiers.
And lastly, at least later in the Roman Republic and through the Empire, the army consisted in large part of auxilia, or foreign auxiliary forces drawn up from allied and conquered territories, which included most of the European countries you are comparing the Roman Army to. So, the reason the Roman Army was so much larger than the English Army is in part due to the fact that the English Army was just one part of the Roman Army.
Question within the question: Were the ancient armies really that big? I am talking about the number 40-80 thousand. I can imagine there being some battles with those numbers, but they would be very rare.