Even after the Internet revolution, listening to music generally required a device -- a CD player, a laptop, an MP3 player -- and a medium -- a CD, a hard drive, flash memory. Then, as fixed and mobile broadband services expanded, people enjoyed increasingly faster access to online content. Streaming, or transferring data so that it can be processed as a steady, continuous stream, became a viable alternative to delivering bandwidth-hungry audio files.
Streaming music services have grown in popularity because they give listeners access to an infinitely large jukebox of songs stored in the cloud. Some providers deliver all of this ear candy as streaming audio only, which means the songs can be played, but they can't be stored locally on your computer hard drive. Others allow for both streaming and downloads. Almost all offer a free service, although you'll have to listen to ads in between songs. If you want an ad-free experience, go for a premium service, which also unlocks other features, such as the ability to access your account on all of your connected and mobile devices.
Finally, the user experience can be quite different from one service to the next. Pandora, one of the most popular streaming music services, works by building a randomly generated playlist based on a song or artist the user identifies. Spotify and Rdio simply open up their music vaults, and let listeners choose.