Pickups/guitar wiring form an LCR (inductance, capacitance, resistance) circuit. LCR circuits can be tuned to have a certain resonance--the above graph shows what that looks like; there's a spike in amplitude for a certain frequency.
If a pickup is wired straight to the jack, that spike is likely to be fairly high, both in amplitude and frequency (which is to say, harsh-sounding). By loading the pickup with additional resistance (pots) and capacitance (for instance, a turned-down tone control or a small loading cap, like .001 uF, in parallel with the pickup), the resonant peak's frequency can be shifted/lowered. (Basically, resistors and capacitors can move around the resonant peak and control how strong it is.) The additional resistance from turning back the volume control slightly or turning down the tone control to some degree will flatten out the resonant peak. But notice that when you turn the tone control all the way down to 0, the capacitor gets involved in the LCR circuit and retunes the resonant peak; turn the tone control up to, say, 2, and the peak flattens again (the capacitor plays less of a role and parallel resistance is doing the work of affecting the resonant peak).
So when people are looking for replacement pickups, they're often (unknowingly) looking for a different resonant peak; a simple tweak of the circuit's capacitance can accomplish that for less than $1! I'd recommend reading Helmut Lemme's 'Electric Guitar: Sound Secrets and Technology,' which explains all of this very clearly.