Microphones can be divided into two general classes: velocity and pressure types. Generally speaking, most velocity mics have a coil of wire attached to a flexible diaphragm which moves slightly when a sound wave strikes it. A magnet near the coil then induces a current in the moving coil that is proportional to the velocity at which the coil is moving through the magnet's field. Because the diaphragm is mechanically soft, it moves a significant (but still microscopic) distance when the wave strikes it. Depending on the details of its construction, the output of a velocity mic can be either a current with only an infinitesimal amount of voltage "pushing" it (in which case it is a low-impedance source) or a high-impedance source (see below).
A pressure mic is one in which the active element is a slab of piezoelectric material so stiff that it moves almost not at all in response to a sound wave, yet still produces an electrical signal which in this case is proportional to the pressure exerted upon it by the impinging wave. That signal is a voltage with only infinitesimal current "behind" it and hence is a high-impedance source.
There are hybrid mic designs out there that blend the characteristics of moving-coil elements and piezos which I can describe if you are interested.