This format of numbers and abbreviations (dB/oct = decibels per octave) is often used to refer to the frequency response behavior of a filter. A filter typically has a cutoff or corner frequency it is tuned to. It then reduces (filters) the frequency spectrum of a signal going through it so that its loudness is multiples of 24 decibels weaker for each octave further away you get from the cutoff frequency.
A 24dB/octave filter is often referred to as a “four pole” filter (as each pole of a filter’s design results in 6dB of attenuation), often used in vintage Moog and Roland synths. 4-pole filters are often associated with subjectively fatter, more “round” sounds than 2-pole filters – but generalizations are always dangerous.