negative freedom is the freedom FROM things, such as coercion by the state or other people. It is the position heald by classic liberals, locke and mill and in a more extreme forms by anarchists, who believe any limit on our freedom is illigitimate.
positive freedom is the freedom TO do things, such as being able to choose your desires and maximise the oportunities avaliable to you. This is the position of welfare liberals, who argue for social mobility. Somewhat stronger are socialists who advocate wealth redistribution and it is also present in essence in the work of marx.
conservatives argue for negative freedon in that they reject the nany state, but positive in that they emphasise comunity cohesion through church family and education.