Power meters are valuable training aides for those serious cyclists who want to improve their power to weight ratios and monitor their wattage output. Watts are the measurement of power used in cycling to determine the strength of a cyclist, with a higher number of watts equating to a stronger rider.
Of course this isn't the be all and end all and power meters should be used in conjunction with other data gathering tools to provide a more overall view of your performance, but the power meter will give you a good idea of your performance in terms of strength.
Power meters usually come as part of a crank arm on the chainring as it measures the force using the power transferred from the pedal in the rotation of the arm to determine the wattage output. Because of this power meters are usually only available on higher end groupsets, as those who choose these are usually more serious about their riding or more invested in the sport.