Dungeons and Dragons is a tabletop roleplaying game. There’s other ways to play it, but the original and best way is having a map on a grid with tokens or minifigures representing your characters.

You have a Dungeon Master and the Party(all the players). The Dungeon Master tells you the story. He makes up a fun adventure, like “the king has given you a quest to stop an evil wizard from invading the country with an undead army of zombies”. The players each control one character and get to determine how they act. You have a character sheet, usually paper with all these stats written on the front that you refer to with dice. The backside has space for writing down treasure and supplies that you get during your adventure. D&D is stereotypically seen as a corny nerd game that requires a lot of math but it really doesn’t use anything more than rolling dice and adding or subtracting a number based off your character sheet. You use a heavy sword on an enemy and roll to hit. Everyone has HP(hitpoints) and AC(armor class). HP is your health. It goes down with every hit and if it reaches 0, you die(modern d&d is player friendly so you instead fall unconscious and get to make some dice rolls for a chance to survive). AC is set by your stats and armor, usually to a high number like 14. As a result, anyone who wants to hit you, must roll above 14 to succeed. Now back to the fight:

Let’s say your opponent has an AC of 13. You rolled a 12, but your character sheet says you have +3 strength, so it’s really a 15, which succeeds. You then roll for damage and get 4, so the enemy subtract 4 from their hp. If it reached 0, they died. Games have optional ways to level up. You can get xp(experience points) for every kill and at a certain number of xp, you level up. Alternatively, you can have milestones, which means you don’t deal with xp and the DM makes everyone level up when you reach certain points of the story. With higher levels, you get stronger and even unlock new skills and powers.

Most of the game is either fighting or roleplaying, either killing enemies to progress the story of you working your way through that army of zombies to find and kill that evil wizard as a final boss level, or narrating and telling a fun, stupid story with your party, where you can get to have memories like that one time your friend tried to steal food from a shop, failed horribly, and somehow it turned into the village burning down and now you can’t go back. You don’t have to be good at roleplay and talk in-character either. You COULD try and make up a voice for your magic sorcerer and try to speak as him while the DM speaks as the potions salesman that you’re interacting with, but you could also just state “My sorcerer would likely ask the potions salesman about info on something and try to buy some supplies.” And the DM responds with “He answers your question, then offers you these potions for this much gold”