We've noticed this behavior ever since deer started getting brave enough to come closer to us. A deer will nod when they know you're looking at them.
Big stag nods his head
Watch this big deer bowing a few times while standing outside our window, looking at us, hearing us talk. He's been fed through that window before.
This behavior is not gender-specific, hinds will do that as well.
When bowing happens, it's usually one deer in your eye focus, knowing they have your attention (and not treats yet! but that should be the other way around!). Our perception is that nodding, or bowing, follows the track of food when it lands. As if the deer is saying:
"This is the game we play, human: you throw whatever tasty thing you got there and I pick it up from the ground. So put it right here, please, I'm ready."
Ultimately, it's hard to say why for certain, but this seems to be the logical reason. They eat with their head down, picking stuff from the ground. They've seen you throw stuff on the ground. They approve of that. In case you've forgotten, they're reminding you what you should be doing: throwing treats under their heads.
Deer who have grown accustomed to taking food directly from our hands often come to prefer that over being thrown stuff. They never nod, they just come as close as possible to wherever they think you might reach them. If they're behind a fence they'll often stick their head through it in an effort to be closer to food than other deer.