We can make wiser policy decisions by asking the libertarian questions no one wants to ask: What protects this program from corruption? What are the unintended consequences? Do we have the right to force others to comply with this rule?
Source: Why Libertarianism Is Not Mainstream (But Should Be) - Foundation for Economic Education
So what is a libertarian exactly? Some would say that anyone who supports any kind of government at all is not libertarian. Really, though, that's just anarchy. I tend to think libertarian means that you support only the minimum amount of government absolutely necessary. That amount may be 0 but we won't really know until we get there. I consider myself libertarian and support slashing government until it starts causing more problems than it solves. Maybe that's 0...maybe it's a little (but not much) more. In any case, it is certainly far, far less than we have today.
Libertarianism could be thought of in a relative way in the following sense. If you believe in a net reduction of government spending, taxation, and/or power, then you are more libertarian than 99% of those in power today.
This article has another pretty good definition. Libertarianism is "skepticism that the government has the authority and competence to solve a wide range of extremely difficult social and economic problems"
I am a Libertarian and the way I explain is that I believe in smaller government than most Republicans do. It is never the government's job to protect us from ourselves nor interfere with free commerce and association. I should be able to do business with whom I choose (or not) and purchase what I choose (or not). Consequences of my decisions are mine to bear. The government is not my parent. I believe the majority of government power should fall on the states as our founding fathers intended. Again, limited power here as well. Seatbelt and helmet laws protect us from ourselves and so need to go in my view. NY and California are perfect examples of tyrannical states. No government should be interfering in the people's daily lives and forcing them to do things they do not want to do. Push agendas on the people. That is tyranny. Libertarians are not anarchists. We believe in limited government both state and federal.