Asteroids in a belt don't stay static from day to day. They lose ore to mining, and during the daily downtime, they slowly regenerate themselves. Belts, similarly, spawn new asteroids to replace popped ones to prevent a wiped out belt from staying that way. However, it's far worse economically and ecologically (space ecologically) to pop a valuable asteroid due to the way asteroids respawn after being popped.
Each system has a set of asteroids that it can contain, in relative numbers. For example, system Example might spawn 90% Veldspar (cheap) and 10% Hedbergite (awesome). That means, if belt 1 in Example needs to spawn one extra asteroid to be full, it's only got a 10% chance of getting a new Hedbergite asteroid at next downtime. If this asteroid is going to replace an old Hedbergite one, that means there's a 90% chance the belt will get less valuable, and a 10% chance it will stay the same. Conversely, if it's replacing a Veldspar, there's a 90% chance the belt will stay the same, and a 10% chance it will get better.
Couple this with the fact that asteroids regenerate their contents every down time, but belts only get new asteroids several days after they get popped, and it's obvious that leaving good asteroids low but still there is better than popping them. This can be taken farther, and a belt can be cultured to have more valuable asteroids. Simply pop (ideally through mining) any asteroids you don't want anymore, and there's a chance they'll respawn as something nicer.
This, of course, is only valuable if you have full or partial control over who uses a belt. Don't bother with this in Empire space, but feel free to practice it in Alliance or backwater corners of Empire space nobody visits.
Edit: This system was debunked by a GM.
"Popping an asteroid doesn't affect regeneration. When you mine an asteroid down, whether it be to a pebble or nothing at all, its ore gets respawned elsewhere in the EVE world. It will regenerate in your own system when it's depleted elsewhere, though due to the mechanics of the regeneration (which I can't go into) it may take a while for the asteroid to resume its former size. There's no rhyme or reason to how quickly it'll respawn; it depends completely on how much ore of that type is mined elsewhere, and where in the respawn order your belt happens to land." - [GM]Abraxas
Basically, not popping rocks has zero effect on regen, it's the 'quantity' of ore mined that gets redistributed back into the game pool from all eve, which is then regen'd AT RANDOM, to all belts in eve.
If a belt is due to get 2k say regend it'll get 2k regened where that be into 1 rock 'placeholder' or into 20 unpopped rock 'placeholders', they are NEVER replaced or downgraded for a different type, so if a belt had 20 rocks of ark it'll always have a min of 20 ark 'placeholders' only 18 may respawn next DT because of the quantity sent to the belt, 2 being dormant which may appear next DT they haven't gone there just wasn't enough allocated to them to make them appear this regen cycle.