Just like many political terms the generalizing nature leads to a lot of confusion. It means different things to different people just like Republicans don't agree on all things Republicans agree with. Someone like Ron Paul who I voted for twice some people argue isn't a true libertarian. I don't usually try and get caught up in all that.
For me libertarian is a freedom thing.
The left claims they are for freedom by allowing things like personal choice when it comes to some drugs and things like abortion. (generalizing) They want their noses in business and many other things and generally want to micro-manage your life. The government can do a better job than you so lets grow it. It's always about how businesses are trying to fuck you.
The right claims they are for freedom by generally trying to stay out of the way on businesses (not always, but generalizing) and some aspects of commerce. But that is quite limited. They were for the bailout. They were for sending stimulus checks in the mail. They are most against this type of shit when they aren't doing it. And they want to control your personal life. They will say shit when arguing about gun control like well why not make murder illegal, oh wait it already is but not apply that same thinking to abortion. Most of the Bible Belt would love to turn us into a theocracy. Why aren't we teaching creationism in science classes type shit. The Bible verse on the Texas run through thing got righties up in arms because how can the government tell those kids they can't have that on their and have their faith? If it was a verse from the Koran....be a whole different story with that crowd. They are the biggest fighters against any faith that isn't their own.
Here is a link to the party platform. I don't agree with everything in there, but you don't really need to imo. At the very least I believe a two party system is always going to be inherently flawed and I wish SOME party would come to at least allow a broader discussion of issues.