Let the great site psk31.com tell it.

“Translated literally, it’s an acronym for “Phase Shift Keying, 31 Baud”. PSK31 is a form of modulation (or “mode”) that offers a new and higher level of performance in conversational communications (keyboard-to-keyboard) that we “hams” (amateur radio operators) can enjoy. And it’s been made instantly usable by all of us, due in part to the proliferation of the personal computer, and in part to the superb and generous efforts of some very talented ham/programmers.

In the short time that PSK31 has been in use, its popularity has grown by leaps and bounds. It may in time replace or at least greatly supplant RTTY and other modes for person-to-person communications. It’s fun, easy, and well worth the effort to get set up, which is not very much at all.”

Or this from Wikipedia:

“PSK31 was developed by English amateur radio operator Peter Martinez (G3PLX), and introduced to the wider amateur radio community in December 1998. Martinez initially called his creation “varicode”, because it uses variable length encodings (Huffman codes) to represent characters.

PSK31 was enthusiastically received, and has since quickly spread into worldwide use. Due to the efficiency of the mode, it has become especially popular with operators whose circumstances do not permit the erection of large antenna systems and/or the use of high power. Also, very little in the way of additional equipment is required (normally just an old PC and a few extra interconnecting cables), and the software is both free to download and will run on older, slower computers.

As the computer is used simply as a ‘means to an end’, the mode has also attracted a new audience of ‘mainstream’ radio amateurs, not necessarily interested in computing or data communications per se. Nowadays on some bands the operating ‘atmosphere’ is less akin to the world of data, and more like that usually found in the morse code sections of the bands. Indeed many operators simply treat the mode as ‘automatic telegraphy’, even adopting long-established morse code conventions, language etc., but using a keyboard instead of a morse key.

PSK31 has also been heard in use on the Citizen’s Band.”

PSK31 Frequency List