"Expanding just a bit on Marakanetz's response, the slope is the decrease in signal strength per octave. So a first order cross-over has a slope of -3db and it goes up from there -- second is -6, third is -12, fourth is -24. The decrease begins at a certain frequency and keeps on going from there depending on the specifics of the cross-over."
Well...not quite. First, 'slope' references the steepness of the plotted falloff of signal strength v. frequency. When someone says 'the slope of the filter', they mean the steepness of the filter when visualized (= plotted on paper). But that term is rather casual and inexact.
A filter point is defined as that frequency which is 3 decibels (dB--the 'B' is capitalized in the abbreviation because it was someone's name) above or below the zero or reference level. A 1st-order filter has a 'slope' or steepness of SIX dB per octave. That means that with a perfectly behaving low-pass filter, the signal strength one octave (= double the frequency) further up the frequency scale is now 9dB below reference level. The signal one octave higher yet (= another doubling of frequency) is another 6dB down, or a total of 15dB, and so on. For example,with a 1st-order low-pass filter of, say, 100Hz, the signal strength will be down 3dB at 100Hz, 9dB at 200Hz, 15dB at 400Hz, 21dB at 800Hz, etc. A 2nd-order filter has a slope of 12dB per octave; a 3rd-order, 18dB per octave, and so on.
In a 2nd-order filter at 100Hz, 100Hz is still down 3dB, but 200Hz is down 15dB, 400Hz is down 27dB, etc. With a 3rd-order, 200Hz is down 21dB, 400Hz is down 39dB, etc.
Higher-order (means 'higher than 1st-order') filters get rid of 'unwanted' signal to a greater degree than 1st-order filters; they're often used to increase power-handling capacity of a driver and hence a system. For instance, if one had a woofer that sounded really poor in the lower midrange because it was slow to respond to faster signals, one could use a 3rd- or 4th-order filter to keep more of the midrange out of that woofer. However, higher-order filters have increasing amounts of phase error, so there's a price to pay.
