Rob Conley (Bat in the Attic) posted what I thought was a good, thorough explanation of OSR gaming for novices. Tim Shorts (Gothridge Manor), in his Friday Question, asked if anyone could do a shorter version. My answer is less substantial than Rob's but a bit more so than Tim's (which maybe makes mine mediocre...). I posted it as a comment on Tim's blog, but after the fact, I decided it wasn't totally terrible, so here it is (with a few tiny stylistic edits) as its own post:
OSR gaming is old-style D&D. One person is the referee, while the others play. As a player, you pretend to be a warrior, wizard, priest or thief, and either a human, elf, dwarf or hobbit. The referee presents you with situations in a fantasy world, and you tell the referee what you say and do in those situations – this can be anything you want. The referee interprets how your words and actions affect the situation. As the situation changes, shaped by your actions, you tell the referee what you say and do again in the new circumstances. Rinse and repeat. Only the referee actually has to know the rules – and even then, the rules are few and designed primarily to help the referee make fair judgments when determining how your words and actions affect the world.
At any rate, that is how I'd probably start an explanation to a novice.