RNS stands for Regulatory News Service, but you'll also see references to "an RNS": an article posted over that same news service. RNS is the official news outlet for the London Stock Exchange (LSE), a commonly used Regulated Information Service.
The Financial Services Authority requires listed companies to provide information to investors via a Regulated Information Service like RNS. News items you're likely to come across in an RNS are changes in the major shareholdings, interim results, changes in director shareholdings, disposals, new share issues, proposed share acquisitions...
RNS has been around since 1988, before then it was called CNS (Company News Service). For the full story - going back to January 1698 and Jonathan’s Coffee House - check out the LSE's
RNS history page.