Adsense is the monetization process used by Google and YouTube to give money, to creators that use it. This is another option for monetization like YouTube Networks.
By adding a Adsense account to your YouTube account, you enable the use of commercials on your video, this commercials may pop up on the side of your video, the bottom and on the video. The more clicks and the more minutes seen on the video, more the money you gain.
Adsense was created by Google back on 2003. It was one of the first ways of income. It was not used on YouTube until 2007, being used ever since.