Bands provided by EQs allow control over a range frequencies. They can range from single to multi-band EQs. For example a three band EQ might have low, mid and high bands. A seven band EQ might have a low-cut, a low, and low-mid, a mid, a high-mid, a high and a high-cut. Fewer bands allow for a more general approach and more bands allow for a more surgical approach.
Sometimes the bands are fixed to a single range of frequencies and sometime they allow this range to be adjusted.
Cuts frequencies below the selected frequency.
Cuts frequencies above the selected frequency.
The Q setting applies to peak filters and changes the width of the peak, making it wider or narrower and therefore making it effect a smaller or larger range of frequencies.
Gain controls the increase or reduction of the frequencies within the band.
If the band uses peaking, is effects only a band of frequencies. With shelf, the selected frequency acts as the edge of shelf, so it effects all frequencies to the left or right of the selected frequency.