The piezoelectric effect is where certain crystalline and ceramic materials have the property of generating an electric current when pressure or a bending force is applied.
This makes them sensitive to acoustic vibrations and they can produce a voltage in response to sound.
Piezo mics (or transducers as they may be called - a transducer is any device that converts one form of energy to another) are high impedance.
This means that they can produce voltage but very little current. To compensate for this, a preamplifier has to be placed very close to the transducer.
This will usually be inside the body of the electro-acoustic guitar.
The preamp will run for ages on a 9 volt alkaline battery, but it is worth remembering that if an electro-acoustic guitar, or other instrument with a piezo transducer, sounds distorted, it is almost certainly the battery that needs replacing, perhaps after a year or more of service.