An audio stream refers to a website that plays music--or other audio--on your computer, but doesn't download the audio to the computer. You can hear the audio while you're on that site, but you won't have access to it once you leave. You can use various capture websites and online programs to convert streaming audio to an MP3 file that you can then play whenever you want, and even download to an MP3 player.
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Use a website like Convertfiles.com (see link in the Resource section) to capture and download an audio stream in the MP3 format. Select the option to download from a website on the main page of Convertfiles, then paste the website address into the textbox. Select "MP3" for the output format, then click "Convert" to get a link that lets you download an MP3 file of the stream.
Download and install My MP3 Recorder (see link in the Resource section) to record streams, especially those that play in a never-ending loop. You can use this free program to record audio onto your computer's sound card and save it directly to the MP3 format on your computer. The program automatically turns off the recording when there is nothing but silence for a few seconds.
Try Zamzar.com (see link in the Resource section) as an alternate capture website. This site is also free to use, and lets you paste in your streaming site info and select MP3 as the output format. Input your email address and the site will send you a link to the converted file.