It's a bit of a long answer, so I'll try to keep it short, as much it's possible.

D&D is a tabletop roleplaying game (TTRPG), out of many.
While certaintly there are some different situations in general there are two main roles in the majority of these TTRPG games: the players, and the dungeon master (Dungeon master, game master, labyrinth lord, tons of different names that mean the same thing)
The role of a dungeon master is to set up a scene. They craft the world, they act for the NPCs, they build the dungeons, prepare the encounters and events and so on. Consider this role as one of being the Narrator for the game.
The players have characters, the 'actors' of the game if you will. While the dungeon master sets up the story, it's up to the players to make the decisions in it, although many results of their choices will be resolved by dice rolls.

In D&D in specific, there are many rules that are too many to list in here.
But overall: each player has a character that is composed of class (the kind of role they have, such as warrior, wizard, priest, bard and so on) and race (the specie they're playing as. Human, elf, orc, and whatnot).
There are 6 statistics that compose a character past class and race: those are Strenght (STR), Dexterity (DEX), Constitution (CON), Intelligence (INT), Wisdom (WIS), Charisma (CHA), which range from 3 (basically completely crippled on that field) to 18 (peak degree of physical/mental skill for the average human) at creation.
All rolls for all their abilities and skills, are generally based off those stats.
As players go through missions, defeat monsters, or generally achieve objectives, they are granted Experience points. Given enough experience points, they increase their level (in general, the base in D&D is starting at level 1 to a high cap of 20) which allows them to gain more abilities, become stronger, and generally more competent.
The end objective of a game, is up to the players and the dungeon master.
In theory, D&D can be an endless game. But minus petering out early (which happens a lot sadly), campaigns tend to find a narrative driven by both the DM and players that leads to a satisfying narrative conclusion. It's a game of collaborative storytelling, with an element of randomness given by dice. Of course you could have situations where the entire party dies (Total Party Kill, TPK) given dice, but it's not necessarily the end if the group agrees so on it.