A so called lossless format. It is the de facto standard for "high" quality audio storage that ensures the highest compatibility amongst different OSs (win, mac, linux). In addition virtually all DAWs and sound editing programs can handle well this format and use it as default.
If you're interested in the inner workings of this format have a look at the excellent wikipedia page: http://en.wikipedia.org/wiki/Wav
This is a similar format to WAV. Once again non-compressed,loseless and using pulse code modulation (PCM), although there are variants that are compressed. In is again in wide usage by software editing programs. It is usually the default format when working with Macs but it is accepted in windows systems as well.
For a detailed description have a look here: http://en.wikipedia.org/wiki/AIFF
This is actually the VORBIS format but it is used in conjunction with the ogg container, hence usually just called "ogg" or "ogg vorbis". It is a lossy audio format but is said to have very good quality compared to other lossy audio formats, especially for low bit rates. More information can be found in the relevant wikipedia article http://en.wikipedia.org/wiki/Ogg_vorbis
This is undoubtedly the most well know audio format. It is a lossy format and as all lossy format a so called perceptual format. The quality varies a lot depending on the settings used in the encoding. In general it is not used in audio editing but is nevertheless used widely on the internet, for streaming, as well as in games. There is a lot of information regarding the MP3 audio format but a good starting point would be as usual the wikipedia article: http://en.wikipedia.org/wiki/Mp3
This audio format is a bit different in the sense that is uses a lossless data compression algorithm. So it can be compressed, usually to 50%-60% of the original size and decompressed to an exact copy of the original audio. It is open ad royalty free but unfortunately does not enjoy a wide support such as the WAV and AIFF audio formats. You can find more information here: http://en.wikipedia.org/wiki/FLAC