The Libertarian Party in the U.S. is a little hard to describe.
To understand it you also have to distinguish the party from the much broader movement. (As with small-i internet for any interconnection of diverse network types versus the capital-I Internet for the particular, big, TCP/IP-based, Connected Internet, some libertarians make the distinction between the small-l libertarian movement and the large-L Libertarian Party.)
Though the libertarian movement has broader roots, the party started as a splinter split off from the Republican party, back in the '60s or so.
It wants minimal government (but not anarchy as some would like to mischaracterize), and maximum individual liberty.
Actually there ARE "minarchist" and "anarchist" wings of the movement, if not the formal party itself. "That government governs least that governs not at all." The split is to some extent between those who think that some government is necessary to defend against attempts at more government (or those who think limited government is the best they can hope to achieve in their lifetimes) and those who think that a little governement is like a little forest fire or being a little bit pregnant.
It's based on a non-aggression principle, somewhat akin to the Golden Rule.
No first use of force. Don't hit first. There's considerable variation after that: Most think that hitting BACK is just fine, but there are pacifist libertarians.
The Party's form of it is this pledge, required of any who would join: "I hereby certify that I do not believe in or advocate the initiation of force as a means of achieving political or social goals." (That's also a sticking point for many who are supporters but not members: For instance, some think that force, threat-of-force, and some kinds of fraud are members of the class "coercion", and that any of the three is justification for the use of force in defense of self or property.)
Most libertarians also think that, once fighting starts, there's no need for proportionality or sportsmanship. (Proportioal response leads to continuous gradual escalation and debacles like the Vietnam conflict.) This is not a game - if you're justified in using force, you're justified in using enough to insure the dispute is settled. The line from Babylon 5: "Never start a fight, always finish one.", might well be a libertarian anthem.
But the non-aggression principle is the ONLY bedrock requirement, so there's a wide range of ideologies under the libertarian tent.
Basically, the idea is that virtually every human interaction should be voluntary. Consenting adults should be allowed to do what they want, but they should also bear the responsibility of their actions.
Libertarians also recognize a right to private property as being necessary for independence. (Indeed, some of them consider that private property starts with one's own body, and derive an ideology of liberty from that.)