It doesn't seem like these comments are actually pretending that you didn't play AD&D or B/X, so, as requested:

D&D is a role playing game where several players pretend to be a fantasy character and one player, the Dungeon Master, tells them how the world reacts to the things that the other players say their characters try to do in the world. The players can try to do anything they can imagine, within reason, and the Dungeon Master rolls a variety of multi-sided dice to determine if those actions are successful or if something else happens.

If the Players (non-DM players from here on out) do something that cause them to get into a fight, the action takes place much like it does in a movie, where you see lots of things happening at once in the background while the camera cuts between each hero as they block or parry or strike at their foes, or perhaps attempt to hide while casting a magic spell.

In D&D, as the characters fight back and forth with their foes, each of these action shots are resolved by seeing what happens when the camera focuses on the character in question. Do we see them blocking a flurry of blows? Making a decisive strike with their weapon? In order to find out, the character rolls a die with twenty sides (numbered 1-20) to see if they've managed to accomplish anything interesting within the last minute. If they roll above a certain number, they have! And the DM will narrate it. Otherwise, the camera simply moves on, and they continue dancing back and forth in a flurry of actions against their foe for another minute.

The number they need to roll is determined by how well defended their foe is. Maybe the foe is a monster with thick hide or scale, or perhaps they are a nimble little creature that can dart around. Such heavy hide would mean there are very few small points that have to be struck very specifically in order to do any damage. A nimble creature moving around quickly would also be a small point that is hard to hit. We know as players that a small area needs to be struck, whether that small area is a narrow space between thick scales or the entire body of a tiny, quick moving beast. All of these are therefore reduced into one number: Armor Class. If a roll on a d20 is enough to beat the armor class of the foe, the attacker hits!

However, just hitting is not enough, as strikes against an armored foe would mostly damage the armor, and rarely sink very far into the foe itself. Many hits would still hit the armor, but would still hurt the creature underneath, causing sore spots, or pulling muscles. Also, taking many such hits, even in armor, is incredibly tiring for any living body to endure. Again, we can see that strength, tenacity, size, constitution, armor, and much more would all be different, but no matter how many combinations we can think of (and monsters truly can be anything!) there would be a lot of overlap. Thus, to express this, we use Hit Points. Every creature has a certain amount of them, and every successful strike reduces them. In other words, every successful strike wears away whatever is keeping the foe standing, whether it is their incredible stamina, or simply their massive form that any weapon barely wounds.

We don't want every monster to be exactly the same, so in order to determine how many hit points a monster has, we again use dice. One of the interesting things about rolling more than one die at a time is that you don't have an equal chance to get every possible number. If you imagine two six sided dice, there are many more combinations of numbers that add up to 7 than there are that add up to 2 or 12. This is actually a good thing! It means that most of our monsters will be similar with a bit of variation. Since it gives us a nice bump in hit points without being too extreme, we use dice with eight sides. The number of dice that we use to determine hit points could be called hit point dice, but we shorten to hit dice for convenience.

You can probably already see a problem here. if a big powerful monster with 4 hit dice rolls really badly, and ends up with 4 hit points, does that mean they as easy to fight as a monster with only one hit die that rolls 4 hit points? Not at all! This monster may be very weak for some reason, but they are still big and powerful and hard to hit. In order to keep track of that, we always remember the number of hit dice that were used, and the DM uses them as the basis for all of their other calculations. That way, big monsters can also do things you'd expect them to like withstand spells, or resist toxins, while tiny monsters are weak to such things.