A hydrophone is a pressure sensor for use in water, and can be visualized as an underwater microphone.
Hydrophones measure pressure changes in water. Microphones measure pressure changes in air. Sound is composed of pressure changes in a fluid medium, whether it is water, air, gasoline, or whatever. Sound can also be composed of elastic stresses in solids like wood, metal, or glass but that is another discussion.
Most modern hydrophones are manufactured using piezoelectric sensors. Piezo sensors possess the unique quality that if you stress the material by bending or squeezing it, a voltage is produced. As the pressure on a hydrophone changes rapidly due to sound, the piezo is stressed and a voltage waveform corresponding to the sound waveform is produced.
Probably the largest market for hydrophones is the geophysical petroleum exploration market. A single marine geophysical survey crew can use 15,000 to 40,000 of these sensors.