In the context of a filter, refers to how sharply the filter reduces or eliminates frequencies past its cutoff frequency. Slopes are usually expressed either in dB per octave, or in "poles", where one pole equals 6 dB/octave. (The terminology comes from electrical engineering; one "pole" is the equivalent of a single passive RC filter circuit. The word "pole" refers to the mathematical equations which describe the behaviors of filters; the subject is far too complex to get into here.)
Most filters used in synthesizers are either 12 or 24 dB/octave, and some can be switched between one and the other. The latter, as might be expected, produces a more prominent effect. The cutoff frequency, by definition, is the frequency at which the output of the filter is 3 dB (a just barely noticable decrease in volume) below the level of the passband. This is where the filter is just beginning to actually filter. At one octave away from the cutoff frequency, a four-pole filter (24 dB/octave) has reduced the output to 27 dB below the passband level; this is usually perceived as about 1/4 as loud as the passband. At two octaves away from the cutoff frequency, the output has dropped to 51 dB below, which will probably be difficult to hear without headphones. At three octaves away, the output has dropped to 75 dB below the passband, which will be imperceptible to most listeners unless the listening level is very loud.