libertarian-A person who advocates liberty, especially in regard to thought or conduct.
socialism-The belief that all property should be held by the state or in common. Since most libertarian socialists are anarchists they believe in property being held in common, meaning anyone can use what ever they want whenever they feel like it.
Basically, while libertarian capitalists believe all force and coercion is wrong unless used to defend one's person or property libertarian socialists believe all force and coercion is wrong unless used to defend one's person, but not one's property since all property was originally founded on theft and relies on state coercion. Without state coercion capitalists would have to create private organizations (basically, miniature states) to enforce property 'rights'. Libertarian capitalists ignore the fact that companies would monopolize land and exclude certain companies, eventually leading to vast tracts of private property that function like modern states do.
see also: anarchism
The Spanish anarchist revolution in the '30s and the Zapatista Revolution today are examples of people trying to achieve libertarian socialism.