Narrowband filters are an essential tool for an astro observer / imager. Emission nebulas, planetary nebulas and supernova remnants all have ionized gas that emit light at specific wavelengths. Using a narrowband filter to observe or image these objects allows you to capture the specific light emitted from these particular objects and exclude all other light around the object. Imaging these kinds of targets with narrowband filters allows for a large gain in the signal to noise ratio while blocking skyglow and shot noise.
The most common narrowband images use 3 filters - Hydrogen Alpha (Ha), Sulfur 2 (SII) and Oxygen 3 (III). Because hydrogen is the most common element in these objects, if you can only obtain one filter, Ha is the hands down choice. With a monochrome camera and RGB filters, it can provide high contrast luminance data for images of these kinds of targets. The specific wavelengths for these filters are:
Ha = 656.3 nanometers (nm)
SII = 672.4 nanometers (nm)
OIII = 500.7 nanometers (nm)
Narrowband filters are defined and sold by their bandpass. These range from 12 nm to 3 nm; the tighter the bandpass, the more unwanted light is excluded and the better improvement of the signal to noise ratio. However, the smaller the bandpass, the more expensive the filter will be. Filters at 12 nm generally cost around $100 each. Filters at 3 nm will be upwards of $800+. As a rule, unless you’re working in a true dark sky area, you shouldn’t need a narrowband filter better than 5 nm and you should be fine with anything between 5 nm and 12 nm.
Finally, narrowband filters should not be used on broadband objects such as galaxies, star clusters, reflection nebula and dark nebula; they generally will not improve the results you get over broadband filters. I will note, however, that Ha filters will be used on galaxies to gather data that will highlight the emission nebulas contained in the galaxy - M33 in Triangulum is an example where the use of an Ha filter with the broadband data is very effective.
Reference: The Deep Sky Imaging Primer 3rd Edition, Charles Bracken