What is a roleplaying game?

A role-playing game is one where a referee presents the player(s) with a hypothetical scenario, the players respond to the scenario and say what actions they would make within it, and the referee adjudicates the results of those actions.

 We do this all the time in our everyday lives, but a roleplaying game provides a set of rules to help the referee structure the game, and manage the chances of success and probable outcomes. In most roleplaying games the player(s) will take on the role of a character or person outside of themselves, and state actions as if that character were doing it.

Many different role-playing games reflect different settings, focuses, and styles of play. For example, Dungeons & Dragons concentrates on Medieval fantasy adventures, while Vampire: the Masquerade chooses modern urban Gothic horror, and Apocalypse World focuses on post-apocalyptic science fiction. Some role-playing games are 'rules heavy', and have a lot of rules that strictly define actions and outcomes, while others are 'rules light' and have a simple set of rules that focus on free-form play. Some take their cues from the war gaming hobby and involve a lot of dice rolling, math and combat, while others focus on a more narrative style in creating collaborative fiction.

It is an immersive hobby that can involve the use of miniature figures, battle maps, pen and paper and dice, or could be just one where a group of people get together to create collaborative fiction. However you choose to play a role-playing game, the most important thing is that you and your group are having fun and enjoying this unique experience.

(every other definition of an RPG I've ever seen has gotten too involved with technical details or comparisons with other gaming hobbies, or misses the point entirely.)