Advantages of digital audio versus analog is the facility of transporting around, as you can fit many cds in a single apparatus. It is also much easier to edit and share. Shooting it is also much simple and only requires a computer and a microphone, nothing more. Analog on the other hand has the advantage of having a single format and it causes no problems of compatibility.
Formats include mp3, which is the most popular and practically THE format for audio. Other formats are wav or wma. Players include iTunes, Windows Media Player or even online audio players, including playlists, like Spotify or Grooveshark.
Audio editing is used in multiple medias like radio, television, cinema, podcasts, interviews and even the most simple videos or audio files use some kind of audio edting.
I myself use audio editing a lot in the process of making my videos. Specially with those that have dialogues and such. Though the music videos don't require any 'pure' audio editing like cutting and moving the audio but I have to control audio levels, and most of the job is in coordinating audio with video. Digital audio editing has allowed many people to make the things they love without the need of expensive and unreachable equipment to make a simple thing like a podcast. And this added with the wave effect of the internet has allowed for a completely new level of interaction between people all over the world.
Some useful pages to look up more information on audio editing and everything to do with it include:
http://audacity.sourceforge.net/
http://en.wikipedia.org/wiki/Digital_audio_editor
http://www.webopedia.com/
https://itunes.apple.com/es/genre/musica/id34
http://www.howtogeek.com/56264/the-how-to-geek-guide-to-audio-editing-cutting-trimming-arranging/
