An acoustic guitar is a guitar that uses only an acoustic sound board. The air in this cavity resonates with the vibrational modes of the string and at low frequencies, which depend on the size of the box, the chamber acts like a Helmholtz resonator, increasing or decreasing the volume of the sound again depending on whether the air in the box is moving in phase or out of phase with the strings. When in phase, the sound is increased by about 3 decibels and when in opposing phase, it is decreased about 3 decibels. As a Helmholtz resonator, the air at the opening is vibrating in or out of phase with the air in the box and in or out of phase with the strings. These resonance interactions attenuate or amplify the sound at different frequencies, boosting or damping various harmonic tones. Also, the air in the box is coupled to the resonance of the top plate. Together, this causes further interaction. The back of the guitar will also vibrate to a lesser extent, driven by the air in the cavity. Some sound is ultimately projected through the sound hole (some variants of the acoustic guitar omit this hole, or have holes, like a violin family instrument). This sound mixes with the sound produced by the front face of the soundboard. All these complex air coupling interactions, along with the resonant properties of the panels, are a key reason that different guitars will have different tonal qualities. The sound is a complex mixture of harmonics that give the guitar its distinctive sound.
No amplification actually occurs in this process, in the sense that no energy is externally added to increase the loudness of the sound (as would be the case with an electronic amplifier). All the energy is provided by the plucking of the string. The function of the entire acoustic system is to maximize intensity of sound, but since total energy remains constant, this comes at the expense of decay time. An unamplified guitar (one with no soundboard at all) would have a low volume, but the strings would vibrate much longer, like a tuning fork. This is because a damped harmonic oscillator decays exponentially, with a mean life inversely proportional to the damping, i.e. the more the volume is increased by the soundboard, the shorter the resulting sound will last.