#2
It's just an extra resistor and capacitor on the tone pot/cap. Your regular tone knob has one cutoff frequency, so as you turn it down it lowers the volume on frequencies above that. It's a pretty low frequency, because it's got to cover a lot of ground, so when you turn it way down, you're cutting a lot of frequencies. With the greasebucket, the two extra parts modify that cutoff frequency as you roll the tone knob down, so that the tone knob modifies higher and higher frequencies as it's turned down while leaving the mids intact, where before they'd be cut.

Simple explanation: It makes the tone knob effect different frequencies, so that when you turn it down it doesn't muddy up the signal so much by cutting lots of the mids and highs in your signal.

Explanation from the tonal point of view: It makes the lower range on the tone pot a bit more useful, but the difference is not great.