Positive and negative liberty
Many philosophers and political theorists distinguish between two concepts of liberty or freedom: positive and negative. The most prominent of these types of discussions has been Isaiah Berlin's 1958 essay on the topic.
The rough difference between the two concepts of liberty is simply this: negative freedom describes one's freedom in terms of lack of oppression (often the State); positive freedom describes one's freedom in tmers of the ability to do pursue various goals. Negative freedom is a 'freedom from' while positive freedom is a 'freedom to'. The labels are assigned because in negative liberty, it describes an absence of interference or obstacles - one is free simply when one has had removed from one's existence all the things which make one unfree. Positive liberty describes some kind of presence that must exist for one to be free: the ability to control and determine one's life, to flourish as a human being.
Politically, classic liberals and libertarians tend to believe that negative liberty provides a complete account of what it is to be free. The logical conclusion of many libertarian critiques of government is that government ought to do no more than Nozick's "night watchman state" - that is exist at the most minimal level required to provide protection from those who attempt to infringe on citizens' freedom from interference.
The political supporter of positive liberty would state that simply existing without interference from others is not sufficient to describe one as free. As well as satisfying one's physiological needs to live in safety, to be free one needs to be able to self-actualize oneself (as Abraham Maslow described it). Given this, state institutions which the libertarian may believe run contrary to the demands of negative liberty can be justified if they help bring about positive liberty. Consider a state-run healthcare system that runs along the lines of the British National Health Service which is "free at the point of use" and funded by general taxation. The libertarian defender of negative liberty would object as the use of taxation to fund the service is a reduction in his freedom from state interference. If one accepts positive liberty, the provision of a service that provides healthcare whenever it is needed means the citizen can go about life in the knowledge that if they get sick they can rely on the nationally-funded health service to treat their illness. Given two citizens in two countries, one with a health service and one without, the one in the country with the health service can go and decide to take part in a somewhat risky contact sport like rugby and rely on the health service to be there if he gets injured - this provision of a health service allows him to make more choices about what he does, and thus contributes to his realization as a self-actualizing human person. Similar accounts of other social services could be described: the provision of education, for instance, enables citizens to decide for them to help themselves choose to take part in a career that matches their interests and aptitudes and thus increases their 'freedom to'.