"Negative liberty is the absence of obstacles, barriers or constraints. One has negative liberty to the extent that actions are available to one in this negative sense. Positive liberty is the possibility of acting — or the fact of acting — in such a way as to take control of one's life and realize one's fundamental purposes. While negative liberty is usually attributed to individual agents, positive liberty is sometimes attributed to collectivities, or to individuals considered primarily as members of given collectivities."~Stanford Encyclopedia of PhilosophyHere is a video from George Smith regarding the notions of Negative and Positive Liberty. The video provides historical examples on these two concepts. Click here to watch.
Here is an analysis from Isaiah Berlin regarding Positive and Negative Liberty. Click here to read.