WMA is the acronym for Windows Media Audio. It is a compressed audio format designed by Microsoft as a (proprietary) replacement for MP3. It includes strong Digital Rights Management support (i.e. DRM that cannot simply be ignored like the 'copyright' bit in an MP3). Windows Media Player previous to WMP 10 only output audio in this format; Windows Media Player 10 provides MP3 encoding as well as WMA, though WMA is still the default.
It is claimed that a WMA file is smaller than a (constant bitrate) MP3 with equivalent sound quality; however, this is mainly from the use of variable-bitrate (VBR) encoding. The true purpose of this format's existence is to lock people who don't know any better into Windows Media Player and its DRM infrastructure. This has happenned more often since Windows Media Player 7 was bundled with Windows ME and Windows XP. Even in 2001, it had been pervasive enough for Napster to trade WMA files as well as MP3s. Successor P2P networks such as FastTrack and WinMX also treat WMA in the same manner as MP3.
A better, open-standard, non-patent-encumbered replacement for MP3 is Ogg Vorbis. Also, the creators of MP3 have created an extension, MP3pro, which has many of the advantages of WMA with few of the disadvantages.