WMA stands for Windows Media Audio. It is a proprietary audio format owned by Microsoft, part of Microsoft's Windows Media technology.
Initially intended to combat the increasingly popular MP3 format, WMA was supposed to be Microsoft's answer to digital music. With the massive influx of constant bitrate, high quality, low file size MP3s flooding the Internet, it soon became clear to Microsoft that they would not be a direct competition for the format.
When you are more acquainted with what the format is, you can get started on how to play it back on your PC.
Windows Media Player
The easiest method is of course to use Microsoft's proprietary media player, Windows Media Player. Windows Media Player comes pre-installed on every Windows machine and will play WMA right out of the gate. Because many Windows users already use WMP as their de-facto media player, it may be smart just to use WMP to playback your WMA files. However, there are many other options if you do not like to use Windows Media Player or prefer another player.
Download the latest WMP here: Download Windows Media Player here.
The second most popular media player must be Apple's iTunes, especially with the spectacular popularity of the Apple iPod line of devices. iTunes plays WMA files, but first it will transcode them on the fly to its own proprietary AAC codec. This is a nifty feature if you sync to your iPod on a regular basis as the iPod will not read WMA files if they have not been transcoded. iTunes is just as popular if not more than WMP and will play WMA files after they are transcoded (very quick process) making it a viable alternative.
Download the latest iTunes here: Download iTunes here.
WinAmp is a lighter, more open media player that plays mostly all types of music formats, and WMA is no different. No transcoding or plug-ins necessary. Just add to the media library or double click and play away.
Download the latest WinAmp: Download WinAmp here.
Foobar is open source, extremely light and will play any audio codec you throw at it. It was an excellent range of plugins as well, but WMA playback is native, as of version 0.9. Foobar is another great alternative to the "big boys" of media players if you don't like all the bloat.
You can download the latest version of Foobar here: Download Foobar 0.9 and above here.
There are also a few video players that playback WMA files without a hitch, via drag and drop or through opening the file. These players are VLC, MPlayer and RealPlayer. You can download each of these as well.