Theoretically, these requirements arise from the way you connect the measurement devices to the rest of the circuit.
A voltmeter is connected in parallel, as you said. Say that you are trying to measure the voltage drop across a resistor RR through which passes a current ii. If the internal resistance of the voltmeter is comparable to RR, then the current ii will be divided through both branches, and the voltage value you read will be different from when the resistor is connected alone. If you make the internal resistance very large, then the current flowing through the voltmeter will be negligible, and the voltage drop across the resistor will not change.
The same applies to ammeter; since you're connecting them in series with the rest of the circuit, you need the device's internal resistance to be negligible so that it doesn't affect the current flowing through the branch. If you connect a voltage source VV to a resistor RR and want to measure the current flowing through the resistor, if the ammeter's internal resistance is not negligible, the total resistance the voltage source "sees" will be different, so by Ohm's Law the current will also be different.