A pickup has inductance, impedance (resistance) and capacitance (not a lot of capacitance, but it plays a part in the pickup's sound). How much of each depends on how the pickup is constructed and with what gauge wire the pickups are wound with. Single coil pickups generally have less inductance, impedance and capacitance than humbuckers. The inductance, impedance and capacitance form an electrical tuned low-pass filter circuit (i.e. frequencies below the frequency are passed, and ones above it attenuated increasingly as the frequency increases), with a boost in output around the filter cut-off frequency.
The volume control pot electrically becomes part of the filter circuit and the higher the pot value, the higher the cut-off filter point (and frequency peak) is. The larger the inductance, the lower the cut-off frequency is. So humbuckers generally have a cut-off frequency and boosted hump in the mids, whilst for single coils, that frequency and hump is in the treble area. One of the two reasons that humbuckers aren't as bright as single coils and have a lot more mids in their output.
Standard choice of pot values for humbuckers is 500k (as this helps keep the frequency peak quite high) and 250k for F-style single coils, as this brings their frequency peak down a bit and stops their sound being too cutting with the trebles boosted.
Because potentiometer values have tolerances, the actual resistance will normally vary by up to ±10% from nominal, so a 500k pot could be between 450k and 550k ohms in value (and a 250k between 225k and 275k). BK promote pots that have a 550k and 280k nominal value, so that ±10% means that the minimum pot value will be at least 500k (or 250k), ensuring that the pickup doesn't sound too dull. In tests, almost everyone prefers the sound of a brighter pickup to a duller one.
In reality, most pots are reasonably close to their nominal value, which is why most manufacturers stick with 500k and 250k values. You can always buy more pots than you need, measure them before use and use the ones with the higher values for volume pots (where the higher resistance has most effect).
Because the volume pot is just part of the filter circuit, and not the whole circuit, increasing the pot resistance further and further gets you a bit more brightness, but it tails off rapidly after about 1Meg ohm. In addition, any additional brightness falls into the high frequency region filtered out by your guitar amp's speaker, so it's not worth going above 1 Meg ohm, even of the most powerful humbuckers (which can be almost all mids with very little treble content).
Lowering of the pot value will make the pickup sound duller and duller, and also reduce the pickup output level as the value goes down, so you generally don't want to stray too far from the standard values unless you want to tame very bright pickups or really try and brighten dull ones.
So, 500k ohms nominal for humbuckers and 250k ohms nominal for single coils. 550k and 280k respecively for the BK pots if you want to guarantee the pickups will be on the bright side.
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