So that you can reroute Mac System audio to other applications such as Quicktime Player for recording purposes, download and install the non-beta version of Soundflower from https://code.google.com/p/soundflower/ (don’t download the one with b in the file name which stands for beta).

Freestyle computers already have Soundflower installed.

1. Launch SoundFlowerBed in the Applications folder
   
2. At the top right of your screen, you’ll see a black flower - click on it and for Soundflower (2ch) select Built-In Output (basically default computer speakers/headphones)
   
3. Now go to System Preferences > Sound > Output and choose Soundflower (2ch) - this will send YouTube or website audio to Soundflower (2ch) which will become the INPUT for the audio recording
4. Get your YouTube or website audio that you want to copy ready to play with 80% to 90% volume which is probably good. This depends on the default volume of the sound source on YouTube or the website.
5. Now launch Quicktime Player (not Quicktime Player 7) and go to File > New Audio Recording
   
6. In the Quicktime Player small window interface, choose the audio INPUT by clicking on the small down arrow and choosing SoundFlower (2ch) which is really Built-In Output coming from YouTube or a website.
   
7. Click on the record button and then play your YouTube or website audio.
   
8. In Quicktime Player, click on the stop button to stop recording.
   
9. Save your file where you want it.

You can then import the file into Garageband, Pro Tools, Reason, After Effects, Final Cut Pro, Premiere Pro, Flash, etc.

You can also use Audio Converter to convert the file into other formats like mp3, wav, etc. if needed.