Explain Like I'm Five

One player is a storyteller called Dungeon Master (DM) who tells the story for other players. Other players are the adventurers, representing characters with their own skills, personalities and alignments. When the story continues, DM might ask the players how they would like to react to some situation, where to go next or what to say to a non-player character (NPC) that DM controls. When a player tries to do something (like push a stuck door open), DM decides if the player has to make a "check" to see if he succeeds or not. Checks involve throwing dice (d4, d6, d8, d10, d12 or d20 mostly) according to player's character's skill on that perticular action, like "strength" in this case. A physically strong character throws bigger/more dice than a weak one in this case. DM pre-decides the sum that the player has to reach with the dice throw, and then the story continues in a different way depending if player succeeded or perhaps failed and triggered a trap, or something. D&D often includes fighting bad guys (or good guys, if you are playing the villains!) which also works with checks and skills, and the players deciding what they are trying to do. Lots of room for improvisation and imagination, which makes the game so fun.