the passband
The passband is the range of frequencies a filter lets through. If a filter is a doorman, the passband is the list of guests who are welcome. For a low-pass filter the passband is everything below the cutoff; for a high-pass, everything above; for a band-pass, the window between two edges. It is simply the part of the spectrum the filter is designed to keep.
By convention the passband is defined down to the -3 dB points: the band edges are where the output has fallen to about 70.7 percent of its peak (half the power). Inside the passband the gain should ideally be flat, the same for every frequency, so the signal passes without coloration. In practice the passband is never perfectly flat. Some filter types deliberately allow a small wobble called passband ripple, measured in dB, in exchange for a sharper cutoff. A 0.5 dB ripple, for instance, means the gain wiggles up and down by 0.5 dB across the band.
Knowing the passband is the first thing you specify when designing a filter: what must get through cleanly. The honest caveat is that the passband edge at -3 dB is not where the signal is untouched; it is already down 3 dB there. If you need a signal truly flat up to some frequency, set the cutoff well above it, and choose a filter type, like Butterworth, whose passband is maximally flat rather than rippled.
An audio low-pass meant to preserve music specifies a flat passband from 20 Hz to 20 kHz. To keep 20 kHz genuinely flat (not down 3 dB), the designer sets the -3 dB cutoff higher, perhaps 30 kHz, so the whole audio band sits comfortably inside the flat region.
The passband is what the filter keeps; its edge is conventionally the -3 dB point, not where the signal is untouched.
The passband edge is the -3 dB point, where the signal is already attenuated by 3 dB. To keep a frequency truly flat, place the cutoff well beyond it.