If I've understood this right ...
It's to do with the number of capacitors/inductors used to make the crossover.
One capacitor/inductor stage makes a simple 2-way splitter to send your signals between the tweeter and woofer. The split point isn't a clean break, it's a gentle slope down and up, and goes at 6db per octave. That is, halves the output for every doubling in frequency beyond the crossover point, on the woofer side.
Using more stages of filter gives steeper changeover points, in steps of 12db (2nd order), 18db (3rd order), 24db (4th order).
Steeper means cleaner separation between what's going to the main driver, and what's going to the tweeter.
"4th Order Linkwitz Riley" tells you how many stages, and the type of filter (or e.g. Butterworth)
Anyone want to correct or expand on that?
