A voltmeter measures the difference in voltage between the two different points (say, on opposite sides of a resistor), but it does not adjust the amount of current passing between these two points through the device. It will therefore have very high resistance, so that it does not draw current through it.

Why should a voltmeter have high resistance?

Answer: a voltmeter measures the voltage difference between two different points (say, on different sides of a resistor), but it should not change the amount of current going through the element between those two points. So, it should have very high resistance so that it doesn't "draw" current through it.

How much resistance does a voltmeter have?

An ideal voltmeter has infinite resistance. Too low of an internal resistance in a voltmeter will adversely affect the circuit being measured.