A "slope" simply tells you have fast a filter is doing its job - for example a 6dB/octave filter will attenuate 6 decibels per octave, a relatively smooth slope...while a 24dB/octave filter will "kick in" a whole lot faster.
A filter with a higher slope, when used as a LPF, for example, will cut off higher frequencies sooner (have more attenuation) than a filter with a flatter slope. Generally, you want a very tight Xover slope.
Just FYI, it can be easier to understand a LPF if you show it as a count down in freq. So if Jmac's thing is confusing, try reading it from bottom to top.