Slope is the setting that expresses how steeply a filter attenuates beyond the cutoff frequency. It is usually given in dB/oct (decibels per octave), and larger numbers mean a steeper cut. When you use a high-pass or low-pass filter to clear out unwanted bands, it affects the result about as much as the cutoff frequency does.
What dB/oct means
12 dB/oct is a rough guide meaning about 12 dB of attenuation for every octave away from the cutoff. Larger values such as 24 dB/oct or 48 dB/oct give a steeper curve. How it actually sounds also depends on the filter design and on resonance.
Gentle slopes
Gentle settings change things naturally and tend to keep the character of the source. Because they act slowly over a wide range, they can be weak when you need to fully suppress an unwanted band. They suit shaping tone.
Steep slopes
Steep settings are useful when you want to strongly reduce low-frequency rumble or high-frequency noise. On the other hand, the tone, the phase, and the impression of resonance around the cutoff are more likely to change. Do not make it steeper than necessary; start from the gentlest setting that meets your goal.
Think of it together with cutoff
What matters is not only the slope but also the frequency where the reduction starts. The same 24 dB/oct gives very different results at a different cutoff. Deciding the frequency, then choosing the slope, then comparing on and off makes it easier to judge.
Points to check
With steep filters, check whether the sound has become thin in exchange for being tidier, and whether it holds up in mono. Use a spectrum display as a support. The role of filters is explained in the EQ article.
