Edit Mode is a feature on YouTube available to content creators, allowing them to edit/cut down their videos.

It was most notably used by matrixlord to remove any drug/sex/atheistic related content in his podcasts.

Apparently, according to a reliable source, if you wish to watch your own YouTube videos, you must do so in edit mode, otherwise you are 'violating YouTube's terms of service' and 'cheating the system', so your account will be permanently terminated.