When it comes to single-player games, I’ve always considered “replayability” to be G-rated shorthand for “fuck-around potential”.
Take GTA3. Most people loved it, and not for its epic storyline, compelling characterization, flashy graphics, or groundbreaking physics engine. They loved it because you could spend two hours – or two minutes – just fucking around to see what sort of havoc you could wreak, totally apart from the actual missions (which were plentiful, and provided a nice distraction for when you finally got tired of fucking around).
Another example, at least for me, was Super Mario 64. Sure, I got all the stars, opened up all the doors, found all the secret areas, spent forever searching in vain for Luigi, and all that jazz. What kept me playing it years after I’d done all that, though, was the ability to move around and interact with the environment in novel and creative ways…in other words, to fuck around. Nearly every time I’d enter a level, I’d find a way to go somewhere I hadn’t been or do something I hadn’t done – slide down a slope to access a lower area, sextuple-wall-jump to the top of a mountain, pick up an object and find somewhere strange to put it – often with comedic result.
(I’ve spent too long on examples already, but I couldn’t let this pass without giving props to San Francisco rush, an otherwise-mediocre racing game memorable for rewarding you for extensive fucking around.)
Now, contrast those to, say, Final Fantasy VII. That was an amazing game by all counts, and I spent days and weeks with it unlocking its various secrets and taking in the storyline and universe. Once that’s done, though…aside from nostalgia or brushing up before watching Advent Children, there isn’t a lot of point to playing it again. The characters, the NPCs, the dialogue, the FMV; they’ll all be the same, and my only reward for trying to fuck around would be a few random battles.
Granted, there are other factors that can contribute to replay value – multiplayer, say, or the “addictive” element of a puzzle game – but when it comes to single-player titles, the word “replayability” is, to me, synonymous with how much fucking around can be done.