what do they do?
'pot' is short for potentiometer they're variable resistance devices that change resistance values as you turn them, 250k means it has a max value of 250 Kohms and same for 500K the bigger the amount of ohms (or resistance) the greater the range or "sensitivity
^ He's right. Generally, 250's are warmer, because they cut more treble. 500's are brighter. Traditionally, 250's are paired with singles, and 500's are paired with 'buckers.
500s also allow more retention of clarity as you roll the tone knob back.