If you own a scope 8 inches or larger then filters can make a big difference to the fine details you see in a range of non-stellar objects. They work by blocking out some wavelengths of light, while allowing full transmission of others. Depending on their type and composition, different nebulae emit light at different wavelengths and by using a filter matched to these the overall background and star brightness is reduced significantly more than the nebulae itself. While all filters cause some overall reduction in light transmission, the differential reduction of the background (especially under light polluted skys) and the transmission of the nebulae’s specific emission lines increases the relative contrast allowing the eye to see more detail than is possible without the filter.
Filters are not magic; their effect is minimal or negative for many objects because of the reduction in total light transmission. However, for some objects – especially marginal ones – the contrast increase can make it significantly easier to make out the details of an object. The Tarantula Nebula in the LMC is one of my favourites to view through a UHC or OIII filter: it reveals different and fascinating details through both. The OIII filter is also ideal for making planetary nebulae stand out from the background stars. NGC2438 in M46 is a excellent example for this.
David Knisely has done an extensive and detailed comparison of the UHC, OIII and Hb filters on almost 100 objects using a 10 inch scope. I’m not going to try and replicate this excellent analysis; instead I recommend you read the descriptions for objects you’re familiar with to get an idea of the improvement you can expect with the different filters.
Many companies make filters. Personally I have the UHC, OIII and Hb 2″ Astronomik filters mounted on a moonlight filter slide with a heater strip and temperature sensor set up to keep them dew free. The filters don’t appear to introduce a colour cast, or any other undesirable artefacts when viewing. They do however require a slight refocusing when changing between a filtered and non-filtered view.
Like many astronomy accessories filters are not cheap, so here’s my buying advice. If you’re only going to buy one filter, get a UHC. Next buy an OIII, especially if you enjoy planetary nebulae. An Hb filter is honestly an excessive luxury, but if you have a big Dob (15+ inches) and you want to be able to enjoy some very faint nebulae objects like the Horsehead it makes a noticeable improvement.