Non-commercial radio is radio stations that do not derive the bulk of their budget from advertising income. The term doesn't strictly mean radio stations with no advertising at all - some non-commercial (or non-comm, for short) stations don't have advertising, but many do have some minimal advertising going on - but rather these stations have ads that are significantly less intrusive and frequent than the ads on their commercial radio station peers.
Non-comm radio stations tend to fund themselves through contributions or a benefactor and may be non-profit. College radio, community radio and National Public Radio (NPR) stations all fund under the banner of non-comm radio.
It is difficult to overstate the importance of non-commercial radio to up and coming musicians - and indeed in some genres, to musicians at all stages of their careers. Why? Advertising dollars might give commercial radio stations a larger audience than (most) non-commercial radio stations, but that ad income comes at a cost - complete control of the playlist. That structure puts commercial radio stations in a position where chasing ratings, to in turn chase advertising dollars, is the end all, be all of their success. Ratings mean people are tuning in, and the bigger the ratings, the more the station can charge for their ad time - which means the station makes more money. Chasing those ratings means they have to keep very tight control on their playlists. They need to devote as a much airtime as possible to mainstream artists identifiable to the widest range of people, so more people will choose their station.
These very strict formatting controls mean that many commercial radio stations have very little time and space to offer artists in the "breaking" stage of their careers - unless those new artists have major label backing, with the majors spending big advertising/touring/promotional dollars and offering extremely enticing promotional deals, like contest sponsorships, to the stations to offset the chance of them taking a risk on a a new artist. If you're a new artist without major label backing trying to get played on a commercial radio station in a large market, you're most likely never going to get that play - and it won't necessarily mean that the station hates your music, it just means that your music is not going to help them achieve the ratings they need to keep in order to keep the advertising revenue coming in (at least at this stage in your career).
At non-comm radio, the picture is much different. Because these stations are not driven by advertising dollars, they don't have to be as obsessed with ratings. Now, that doesn't mean that ratings don't matter at all to non-comm stations or that these stations will play any old thing that crosses their desk. What it does mean, however, is that these stations have significantly more flexibility when it comes to determining their playlists. These stations can give the local bands their first airplay, play the music of the up and coming touring bands passing through town and provide an outlet to niche music genres that don't often draw enough of a radio audience to allow them to sustain commercial radio stations. Non-commercial radio is both a foot in the door for musicians and the only radio outlet over the course of a career for other musicians - especially, for instance, in genres such as bluegrass and jazz.
Aside from the niche genres, non-comm radio offers another benefit for up and coming musicians - a track record of radio plays that can then be used to start promoting to commercial radio. If a musician mounts a successful non-comm campaign, such as a college radio campaign that lands then on the CMJ charts, the commercial radio stations will start paying attention and start looking at them as a radio asset.
Understanding the difference between non-commercial and commercial radio is key to planning a great PR campaign for a new release. Learn about that difference and much more in Radio Basics: 101 Guide.