What is Dungeons and Dragons®?
Dungeons & Dragons® (D&D®) is a collaborative story-telling role playing game (RPG), where you and a group of other players tell a story together around a table.
The player is you, who make up the bulk of the people sitting around the table. You will play the role of a character, oftentimes a heroic one, which you create (if you’re new to the game, someone might create one for you to get you playing quickly).
The other player at the table is called the game master (GM) or dungeon master (DM), of which there is typically only one. (S)he is the player who provides the backbone and narrative thread of the story, and who guides your heroes through quests for treasure, battles with deadly foes, daring rescues, courtly intrigue, complex negotiations, and much more. Sometimes there are co-GMs, one who does what is described above and another that plays various non-player characters (NPCs).
The story that is played around the table is not at all pre-determined. The GM provide a skeleton of a story, sets the scene, asks what each of the characters are doing, then adjudicates the result (often using dice). The players provides the builk of the story through playing their characters. Each character has things they're good and bad at, and by rolling dice you determine if you're successful in various things in the world, like negotiating, hiding, attacking or casting a spell.
So, as a group you play through the story-teller's world and a shared story experience that everyone contributes to.
Here is a great article that explains things more or you can watch these awesome videos created by players who just love the game.