R.S.A. stands for Rivest, Shamir and Adleman - the three cryptographers who invented the first practical commercial public key cryptosystem. Today it is used in web browsers, email programs, mobile phones, virtual private networks, secure shells, and many other places. Exactly how much security it provides is debatable, but with sufficiently large keys you can be confident of foiling the vast majority of attackers. Until recently the use of RSA was very much restricted by patent and export laws. However, the patent has now expired and US export laws have been relaxed.
Further ReadingTwo books I found very informative on this subject are: