Regular, 'non-smart' electricity meters have been around since the early 1900’s without too much change to the way they measure how much power is being used.
A detailed technical explanation of exactly how they work isn't necessary, but the best way of explaining them is to describe them as a small electric motor, which runs faster as more power is used. The motor is in fact a disk about which two coils (one for current, one for voltage) have been placed. The rotating disk drives the meter, giving the total of energy consumed in a billing period.
In that respect, electricity meters work very similarly to water meters, which tick faster as more water flows. The totting up by means of gearing is pretty much identical between water and electricity.
Replacement of regular meters with smart meters
Regular electricity meters are gradually being replaced around Australia by smart meters. Smart meters are all electronic - no moving parts. Smart meters are necessary for solar systems with feed-in tariffs, and depending on how they're made, can be used to help automate, control and monitor energy usage in your home.
Many state governments annouced that smart meters would be rolled out by the electrical distribution companies throughout 2014. If you still have an old-style analogue meter, contact your electrical provider.