Music PR - press relations - is the promoting of a new release, tour or other music related news to the media. People who work in PR liase between labels and/or musicians and the media to try and get album reviews, profiles of the band, reviews of live shows and so on. Most music PR companies have a dedicated focus - for instance, they only do print media or they only do radio. Some are divided even further, in that they only do college and club radio promotion or they only promote to websites.
Most music PR is done on a campaign basis. If a label wants to promote a new release, they may hire a PR company for a set window of time, during which the PR company will try to generate as much press as possible. If the band will be touring during that time. sometimes the PR firm will also do a round of press for the tour, or sometimes they will charge an extra for that (especially in the case of large PR firms/large record labels). At the end of the campaign, the PR company will issue a report with press clippings of all of the coverage the album has received. They may report at intervals during the campaign as well.
Hiring a PR company can be a great thing. When you're working with an established PR company, then you know that first hurdle - the building of press contacts - has already been tackled. An envelope bearing the logo of a well known PR company can carry a lot of weight at a magazine that received hundreds of promos a day. Working with these companies can be extraordinarily expensive, however, and there is no guarantee of any pay off. Some PR campaigns end with exactly zilch in the way of press, but you still have to pay the bill. For this reason, small labels should think carefully about PR - much of it can be done in-house, so only hiring a PR company when you think you have something that could really get a lot of press is a good plan.