in short, libertarianism is the philosophy of freedom. it advocates for all and in every situation, freedom from the coercion of others. a libertarian believes that a person who does not initiate force against another person, should be free from the initiation of force from others.
it's basically what each child is taught by parents at an early age, "don't hurt others if they haven't hurt you". seems simple, right? then it may come as a surprise that the vast majority of people utterly oppose this doctrine in practical reality.
it may be helpful to start off with some definitions:
rights: the entitlement to do with one's person or property what one wishes up to the boundaries of the person or property of others
property: those items belonging to an individual beginning with one's own self, attained in a non-coercive manner.
coercion: the use of force or violence, fraud or the threat of the use of force.
initiation of force: the act of first coercion against the rights of others.
a libertarian believes that it is morally wrong and deleterious to civilized society to initiate force upon others. to be clear, this does not include the use of force in defense, which is why we refer to the initiation of force, rather than retaliation to force.
for example: one day you are walking down the street and a person approaches you, stops you and says, "i have a gun. if you give me your wallet, i won't shoot you." this person has used threat to initiate force upon you. in other words, he started it. if your response is to tap him on the head with a pipe, you have responded to his force in defense, which is acceptable.
the difference between a libertarian and anyone else is that a libertarian consistently opposes force initiation (called the non-aggression principle). all non-libertarians sometimes oppose force initiation, but sometimes approve of it. the non-libertarian may scoff at such a statement. "i'm not a libertarian and never support criminals robbing others!" ah, but they do! when the idea becomes more abstract, the non-libertarian may not recognize the initiation of force for what it is - and that is where the next post will begin.