The expansion bottle/reservoir is not filled upto the neck. When the engine warms up, the temperature of the coolant increases and as per Charle's law, volume is directly related to temperature, so volume of the coolant also increases, it exerts more pressure inside radiator. When the pressure exceeds particular point (written on radiator cap), the pressure relieve valve of radiator cap opens and some coolant travels towards expansion bottle. That coolant is sucked backed into the radiator when engine cools down.