Why do the water pipes around my water meter vibrate when water is flowing?
Hearing a small amount of noise from a water meter vibrating is not uncommon, however if the noise is loud enough to be distracting, you may have a worn impeller in the meter. You can try holding the meter securely or applying some pressure to the meter to see it that reduces the noise, but also you will be able to feel if the vibration is coming from the meter itself.  If simply holding the meter or the lines attached reduce the noise to an acceptable level, then securing the pipes to a wall bracket or clamping them securely may be all you need to do.  If this test does not lower the noise and you can feel the vibration through the meter housing, then I'd suggest calling your water utility company.  They own the meter and would come out to replace it if necessary, usually at no cost to the consumer.