High Pass, Low Pass, Notch, and Notch Width

A 'notch' filter is one that only affects a single frequency
rather than a range. 'Notch width' is also referred to as
the 'Q' of the filter. It refers to the effect of the filter
on the nearby frequencies surrounding the 'notch' frequency.
You may want to refer to the recent Stereophile review of
the Rives room EQ which is essentially a 3-band notch
filter. You'll get a rundown of all the terms you mention
here. I'm guessing the 'notch' filter was included on your
pre/pro to tame the worst resonant node (usually in the
bass region) present in your room.

A high pass filter will progressively roll off (cut the amplitude of) the response below the set frequency, letting the frequencies higher than the set frequency 'pass' unaffected.

A low pass filter will progressively roll off (cut the amplitude of) the response above the set frequency, letting the frequencies lower than the set frequency 'pass'.

Low or high pass filters can also be known as 'shelving' filters if the attenuation rate above or below the set frequency (also known as the 'knee' of the curve) is fairly steep, a reference to the 'shelf'-shaped graph of the resultant response. The affected frequencies are then said to be 'shelved' down.

A 'notch' filter will affect a relatively narrow band of frequencies both above and below the set 'center' frequency, while leaving the bandpass response at the frequency extremes (high and low ends of the audio spectrum) unaffected. The term 'notch' usually means an amplitude cut, but the same idea can also apply to an amplitude boost, or 'spike', around a set center frequency. The width of the notch or the spike, meaning how steep or broad the shape of the amplitude curve is to either side of the center frequency - which in turn implies how large a range of frequencies the filter will affect - is also known as the filter's 'Q' setting.