Adsense is the monetization process used by Google and YouTube in order to give money to the creators that use it. This is another option for monetization like YouTube Networks.
By adding an Adsense account to your YouTube account, you enable the use of advertisements on your video. These advertisements may pop up on the side of your video, the bottom or on the video, while it's playing. The more clicks and the more minutes seen on the video, more the money the creator gains.
Adsense was created by Google back in 2003. It was one of their first ways of income. It was not used on YouTube until 2007, being used ever since, the quantity of money given to content creators has been increasing every year since launch.