Streaming audio is a way of listening to a music file from a remote source (like somebody else's website) without downloading it to your computer. It's convenient because you don't have to wait long for a piece of music, you simply click, wait a couple of seconds and the song plays. The downside is that streaming files are temporary and will be deleted as soon as you shut down your computer.  Only non-streaming files (such as an mp3) can be saved on your computer.

mp3 files are storable on your computer.  Once you download them to your computer they will stay on your hard drive even after you have left the website. They are also of better sound quality than the streaming audio files. The downside is that they can take a while to download depending on the speed of your internet connection.

The long and the short of it.
If a website offers you both Streaming RealAudio and an mp3 file of the same song:  Listen to the music first on the streaming audio.  If you should decide you'd like to keep it, take a few minutes more and download the mp3 version.

How long do I have to wait for an mp3 to download?
If your computer uses a slower internet connection speed (a dial-up modem) Windows Media Player will start to play a non-streaming music file (mp3) before it is completely loaded onto your computer, playing a piece of music as it arrives to your computer from the internet, a few seconds at a time. The song starts and stops. When you download a non-streaming (mp3) file, wait for the song to be completely downloaded to your computer before you play it.  Just click "stop" on whatever player you are using and wait until the file is completely loaded.  It will most likely begin to play automatically one the download is complete.  The length of time it takes to download a file will depend on the speed of your internet connection.