A Bass reflex system (also known as a ported, vented box or reflex port) is a type of loudspeaker enclosure that uses the sound from the rear side of the diaphragm to increase the efficiency of the system at low frequencies as compared to a typical closed box loudspeaker or an infinite baffle mounting.
A reflex port is the distinctive feature of a very popular enclosure variety. The design approach enhances the reproduction of the lowest frequencies generated by the woofer. The port generally consists of one or more tubes mounted in the front (baffle) or rear face of the enclosure. Depending on the exact relationship between driver parameters, the enclosure volume (and filling if any), and the tube cross-section and length, the low frequency limit or efficiency can be substantially improved over the performance of a similarly sized sealed box enclosure.
Though helpful with extending bass performance, bass reflex cabinets can have poor transient response compared to sealed enclosures at frequencies near the lower limit of performance. Proper adjustment of the cabinet and port size, and matching with driver characteristics can reduce much of this problem.
Unlike closed box loudspeakers, which are substantially airtight, a bass reflex system has an opening called a port or vent, generally consisting of a pipe or duct (typically circular or rectangular cross section). The air mass in this opening resonates with the "springiness" of the air inside the enclosure in exactly the same fashion as the air in a bottle resonates when a current of air is directed across the opening. The frequency at which the box/port system resonates, known as the Helmholtz resonance, depends upon the effective length and cross sectional area of the duct, the internal volume of the enclosure, and the speed of sound in air.
When this vent air mass/box air springiness resonance is so chosen as to lie lower in frequency than the natural resonance frequency of the bass driver, an interesting phenomenon happens: the backwave of the bass driver sound emission is inverted in polarity for the frequency range between the two resonances. Since the backwave is already in opposite polarity with the front wave, this inversion brings the two emissions in phase (although the vent emission is lagging by one wave period) and therefore they reinforce each other. This has the useful purpose of producing higher output (for any given driver excursion compared to a closed box) or, conversely, a similar output with a smaller excursion (which means less driver distortion). The penalty incurred for this reinforcement is time smearing: in essence the vent resonance augments main driver output by imposing a "resonant tail" on it. For frequencies above the natural resonance of the driver, the reflex alignment has no influence. For frequencies below the vent resonance, polarity inversion is not accomplished, and backwave cancellation occurs. Furthermore the driver behaves as though suspended in free air, as box air springiness is absent. This is a far more significant problem with vinyl record replay, because in this case there may be significant subsonic content in the audio signal, due either to warped records, or to turntable suspension wobbling or acoustic feedback.
When speakers are designed for home use, manufacturers often consider the advantages of porting to outweigh disadvantages. The design is popular among consumers and manufacturers (speakers cabinets can be smaller and lighter, for more or less equivalent performance) but the increase in bass output requires close matching of driver, the enclosure, and port. Poorly matched reflex designs can have unfortunate characteristics, making them unsuitable for settings requiring high accuracy and neutrality of sound, e.g. in monitoring facilities, recording studios etc.
The effect of the various speaker parameters, enclosure sizes and port (and duct) dimensions on the performance of bass reflex systems was not well understood until the early 1960s. At that time, pioneering analyses by A.N. Thiele  and Richard H. Small related these factors in a series of "alignments" (sets of the relevant speaker parameters) that produced useful, predictable responses. These made it possible for speaker manufacturers to design speakers to match various sizes of enclosures, and to match enclosures to given speakers with great predictability. All of this is constrained by the laws of physics, which is covered in detail in Thiele and Small's work. It is not possible to have a small speaker in a small enclosure producing extended bass response at high efficiencies (i.e., requiring only a low-powered amplifier). It's possible to have two of these attributes, but not all; this has been termed Hoffman's Iron Law after J. Anton Hoffman of KLH. The sound pressure produced depends upon the efficiency of the speaker, the mechanical or thermal power handling of the driver, the power input and the size of the driver.
Such a resonant system augments the bass response of the driver and, if designed properly, can extend the frequency response of the driver/enclosure combination to below the range the driver would reproduce in a similarly sized sealed box. The enclosure resonance has a secondary benefit in that it limits cone movement in a band of frequencies centered around the tuning frequency, reducing distortion in that frequency range.
By their own nature, resonant systems cannot start and stop instantly. Ported speakers stagger two resonances, one from the driver and boxed air and another from the boxed air and port, in order to achieve their bass output, a more complex case than an equivalent sealed box. This causes increased time delay (increased group delay imposed by the twin resonances), both in the commencement of bass output and in its cessation. Therefore a flat steady-state bass response does not occur at the same time as the rest of the sonic output; rather, it starts later (lags) and accumulates over time as a longish resonant "tail". Because of this complex, frequency-dependent loading, ported enclosures generally result in poorer transient response at low frequencies than in well-designed sealed box systems.
Another trade-off for this augmentation is that, at frequencies below 'tuning', the port unloads the cone and allows it to move much as if the speaker were not in an enclosure at all. This means the speaker can be driven past safe mechanical limits at frequencies below the tuning frequency with much less power than in an equivalently sized sealed enclosure. For this reason, high-powered systems using a bass reflex design are often protected by a filter that removes signals below a certain frequency. Unfortunately, electrical filtering adds further frequency-dependent group delay. Even if such filtering can be adjusted not to remove musical content, it may interfere with sonic information connected with the size and ambiance of the recording venue, information which often exists in the low bass spectrum.
Whether or not the effects of these in a properly designed system are audible remains a matter of debate. A poorly designed bass reflex system, generally one that is tuned too high or too loosely, can ring at the tuning frequency and create a 'booming' one-note quality to the bass frequencies. In effect, this is due to the port resonance imposing its characteristics to the note being played, and is grossly exacerbated if the port resonance coincides with one of the resonant modes of the room, a not unusual occurrence. In general, the lower in frequency a port is tuned, the less objectionable these problems are likely to be.
Ports often are placed in the front baffle, and may thus transmit unwanted midrange frequencies reflected from within the box. If undersized, a port may also generate "wind noise" or "chuffing", due to turbulence around the port openings at high air speeds. Enclosures with a rear-facing port mask these effects to some extent, but they cannot be placed directly against a wall without causing audible problems. They require some free space around the port so they can perform as intended. Some manufacturers incorporate a floor-facing port within the speaker stand or base, offering predictable and repeatable port performance within the design constraints.
Port compression 
Port compression is a reduction in port effectiveness as sound pressure levels increase. As a ported system plays louder, the efficiency of the port reduces, and distortion emitted by the port increases. This can be reduced by port design, but not totally eliminated.
Asymmetrical loading of the driver cone during high level usage can be reduced by placing a baffle at the inside end of the port tube. This baffle can also serve as a stiffening structural element of the enclosure.
See also 
- Thiele, A. N., "Loudspeakers in Vented Boxes: Parts I and II," J. Audio Engineering Soc., Vol 19, No. 5, May 1971, pp 382-392 (Reprinted from a 1961 publication in Proc. IRE Australia).
- Small, Richard H., "Vented-Box Loudspeaker Systems, Part I: Small-Signal Analysis", J. Audio Engineering Soc., Vol 21, No. 5, June 1973, pp 363-444.