How to create a video with audio comment? I want to make a tutorial video where I explain something. 
In most commercial video editors, there is the possibility to see a video and to start a live audio record.

Is something like this also possible with Blender, or do I have to record my commentary separately outside of Blender, and then hope that video and audio fit together?
Blender has no audio recording functions. You could simply play your animation and record with Audacity to MP3.

The recordings can be arranged in Video Sequence Editor (VSE) to synchronize them with the video , it might be helpful to record a each few sentences to a separate files.

Image of the VSE while moving around audio tracks: