the stopband
The stopband is the range of frequencies a filter is meant to block. If the passband is the welcome list, the stopband is the do-not-admit list. For a low-pass it is everything well above the cutoff; for a high-pass, everything well below; for a notch, the narrow band around the notch frequency. It is the part of the spectrum you want gone.
No filter blocks the stopband perfectly, so we specify how much rejection is enough with a number called stopband attenuation, in dB. For example, you might require that any frequency above 10 kHz be at least 60 dB down, meaning reduced to one part in a thousand of the passband level (60 dB is a factor of 1000 in voltage). Between the passband edge and the point where the stopband attenuation is first met lies the transition band, a no-man's-land that is neither fully passed nor fully blocked. A steeper filter has a narrower transition band.
The stopband specification drives most filter design choices. The classic example is the anti-alias filter before an ADC: any energy above half the sampling rate must be pushed deep into the stopband, or it will fold back and corrupt the signal forever. The honest caveat is that deep, narrow-transition stopbands cost something, more filter order, more parts, more ripple or phase distortion, so you specify only as much rejection as you truly need, never an imaginary brick wall.
Sampling audio at 48 kHz means the Nyquist limit is 24 kHz. The anti-alias low-pass passes up to 20 kHz but must drive everything above 24 kHz deep into the stopband, say 80 dB down, in only a 4 kHz transition, which forces a high-order filter.
The stopband is what must be blocked; how deeply, and how narrow the transition, sets the filter's difficulty.
Stopband rejection is finite, never infinite. Demanding both very deep rejection and a very narrow transition forces a high filter order, which brings more parts, ripple, and phase distortion. Specify only what you need.