Basically a band pass box come in two varieties, 4th order and 6th order. The orders refer to the slope of fall off either side of the tuning frequencies. but both are a box divided into two compartments with the sub firing into the other. A 4th order bandpass box has a sealed sub compartment with a front comparment on it that is vented. Normally the vents are large enough to be able to see a sub but normal round ports can also be used. A 6th order bandpass box has a vented sub compartment and vented front compartment. Bandpass boxes are chosen when you need to tune the response or maximise the output over a chosen frequency range. Generally they are more effcient than a sealed or vented box so produce more bass for a given input. It's the same princaple you would use when firing a sub into a corneer of the boot to maximise it's output (ie boundary gain). You can also tailor the rate at which the efficiency falls off to better minimise sub 20hz output and that over the 80hz (or whatever your chosen level is) crossover point to the front seakers. Also vented boxes are more effcient than sealed boxes.