The voltmeter is connected parallel to a component of the circuit. This means the resistance (or impedance) of that part of the circuit is going to change, which in general changes the potential drop across the component. This effect will be larger if the voltmeter has lower resistance (to the point of completely ignoring the component if the voltmeter resistance goes to zero). Thus, in order to get an accurate measure of what the potential would be without the voltmeter, it needs to have a high resistance.
