That’s a question with a complex technical answer.
Without going into too much detail of electronics, electronic components have various characteristics which work together to affect the signal. The pickups may, for instance, have a high or low output depending on the construction.
Resistance is, like it sounds, something which “resists” the flow of electrical signal.
For the “volume” control on the guitar, the resistance (measured in ohms, symbol Ω) between the input from the pickups and the output jack will affect how much of the signal gets through: the bigger the resistance, the less signal get through. The volume control is a potentiometer (or “pot”) which is, basically, a variable resistance device which goes from low resistance to high resistance. The rating is the highest resistance that the pot will go to.
So a 250kΩ pot will adjust between (approximately) 0 Ω to 250kΩ (kΩ is 1,000 Ω). When you turn the volume fully “up”, to allow the maximum signal to be sent to the amp, the resistance of the pot is nearly 0Ω. When you turn it fully off, the resistance is at the maximum (either 250kΩ or 500kΩ).
At the halfway point, it’s somewhere between the two. A linear 500kΩ pot will have a resistance of around 250kΩ at its halfway setting.
If you compare a linear 500kΩ and 250kΩ pot as a volume control, turning down a 500kΩ pot will reduce the output level approximately twice as quickly as turning down a 250kΩ pot.
Or, put another way, the 500kΩ pot set halfway will be the same signal level as the 250kΩ pot when fully off.
The impact on the tone control is similar, although it’s a fair bit more complex to explain why.
Basically, the other components, especially the pickups. As i said, pickups can be high or low output (or somewhere inbetween).
If you, for instance, use a 250kΩ pot with a high-output pickup where a 500kΩ pot should really be used, then you could find the volume control of the guitar won’t turn fully off.