Bandwidth can be described as the total frequency range that can be passed by a specific filter or amplifier. Bandwidth is measured in Hertz (Hz) and a common bandwidth is 20Hz-20KHz, which is the natural hearing range of the human ear.
In relation and in context to synthesizers, you will come across the term passband bandwidth, this describes the difference between the upper cutoff and lower cutoff frequencies of a bandpass filter.
When talking about EQ (equalization) in music production, you will find two terms that are called Q factor and Bandwidth. In summary, the number of frequencies (known as the bandwidth) that will be cut or boosted by the EQ is controlled by the Q factor.
A low Q factor will result in a wider bandwidth, this means that a wider range of frequencies will be affected. A higher Q factor will result in the opposite, a narrow bandwidth with a fewer range of frequencies being affected.
Using these Q factors can be useful in removing unwanted noise in your music, things like clicks and string scrapes. However, it must be used carefully as too much filtering of frequencies can create an unnatural sound and lose the overall balance of your music.