The transfer function of analog filters is largely determined by the ratio between the passband and the stopband. The transition from the passband to the stopband is given by the filter slope or the edge steep ness of the filter. The slope in turn depends on how many poles such a filter has. If such a filter is single-pole, then it is a 1st order filter and the slope is 6 dB/ octave.
A 1st order analog filter corresponds to an RC element, a combination of a resistor (R) and a capacitor (C). If two RC elements are connected in series, the slope increases to 12 dB/octave. It is then a 2nd order filter. With five RC elements, it is a 5th order filter whose slope is 30 dB/octave.
The higher the order of a filter, the steeper the slope.