| "4th order" refers basically to the type of box. For example:
A "1st order" enclosure is an infinate baffle setup where there is no box used. This type has the least interraction with the function of the speaker.
A 2nd order enclosure is your typical sealed enclosure. The sealed enclosure has an effect on the function of the driver within it.
A 3rd order enclosure is a ported box. The box and the port play a role in the overall output.
A 4th order enclosure is your typical "bandpass" box. It's got a sealed chamber, and a ported chamber.
There are 5th, 6th and even 7th order bandpass style enclosures that are way too far beyond my comprehension level for me to explain.
So.. the 4th order bandpass "effect" is more or less just a description of the output from that type of enclosure. With a bandpass box, it does just as the name implies. It only allows a narrow band of frequencies to pass. A bandpass box will produce a sharp low-frequency roll-off, much like a ported box except even more rapid. Plus, because the only source of output is through the ports, and not directly from the driver surface, you also have a very sharp high frequency roll-off. The result is a narrow frequency band of sound. This can be a very positive feature when designed right. Filtering out all high frequencies with the enclosure instead of with an electronic/passive crossover has some advantages. Mainly, it also filters the mechanical harmonics produced by the driver itself. Play a 100hz signal, and you get output at 200hz, 400hz, 800hz, etc. The driver itself will resonate at the upper harmonics. Plus the driver may buzz, or rattle, or whatever. All of this is filtered with a bandpass box. This helps the bass sound like it's coming from up front with the rest of the sound, instead of in the back of the car. The drawback is that because you can't hear the mechanical distortion from the speakers, people tend to blow them up because they don't get that tell-tale clunk, bang, or distortion that you usually get before you destroy a speaker.
Another advantage is that within the bandpass range, your output sensitivity is greater with a bandpass box than with a different style. Higher sensitivity = more output for a given power level.
The drawbacks to bandpass enclosures are that they are absolutely enormous (a big drawback in a thirdgen), and that they need to be built specifically for your drivers or they sound like ***. Just buying a pre-built bandpass box and stuffing your subs into it almost never produces good results. You wind up with an output that has a VERY narrow frequency band, and winds up being a one-note-wonder. At some frequency (say 60hz, although it'll be different with every configuration) it'll pound like hell, but at any other frequency, it sucks. All bass you hear will be 60hz bass. Not very musical. | 
