Why Current, the flow of charge measured in amperes, is measured with an ammeter. An ammeter is connected in series with the circuit so all the current being measured flows through the meter, and it has very low internal resistance so it does not disturb the circuit. The name matches the unit: amperes are read on an ammeter.
Watch out A voltmeter measures potential difference and connects in parallel across a component; an ohmmeter measures resistance and must be used on an unpowered circuit.
Amps -> ammeter, in series. Volts -> voltmeter, in parallel. Ohms -> ohmmeter, power off.