What is "slope"???

I dont think I totally understand the properties of slope?

I'm setting up a Theta Casablanca and when it comes to crossover I get it,....but as far as setting the slope, Im at a loss as to what it addresses.

Please help me understand what I should be listening for.

I think 1st is 6 db (decibal) an octave roll-off, 2nd is 12, 3rd is 18, and 4th is 24db an octave roll-off. That's the slope at which the signal is rolling-off With 90 degrees phase shift on each one going up also.
"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.
OK, so the second part of my question was..

What should I be listening for to establish the proper slope for my processor?

Please be as straight forward as possible.

Thanks for the help!
M, is this a high- or low-pass filter? Do you have large, full-range speakers or ones with relatively limited bass output? Do the main speakers have plenty of power-handling capability full range or can you overdrive them at YOUR normal, high listening levels?
My speakers are full range Thiel 2.3's. They are capable of full range bass, but I cross them over at 80Hz to my sub. I find it allows the Thiels to do what they do best.

The slope options available are 6db, 12db, 18db and 24db

Hope this helps.