> When I hear the word, I think of someone who believes they (and everyone) should have the right to do whatever they like - so long as it does not infringe on anyone else's freedoms or rights.
I've always hated this definition, because it's so empty. The whole debate of politics is what happens when the freedoms and rights of different people come into conflict. Different groups define these freedoms and rights differently, and think different responses are appropriate when there is conflict.
The difference between a libertarian and say a conservative is not that one believes people should be free to do what they want and the other does not. It's that one defines "freedom" narrowly and the other defines it more broadly.
Take something like prostitution. A libertarian would say you have the freedom to sell your body or to buy sex for money. A conservative might believe that people should have the freedom to create cohesive communities based on traditional values, and having your kids see prostitutes on the side of the road undermines that. Similarly, the two react differently when coercion in prostitution brings the prostitutes' rights in conflict with her pimp's. A libertarian might say that we have other laws to deal with abuse and coercion and that banning prostitution is unnecessary. A conservative might note that such abuse is endemic to prostitution and that banning prostitution could prevent the burgeoning of an extremely abusive and coercive business. A liberal might swoop in and say we should legalize prostitution, but regulate it to prevent the downsides.
Or consider something like workers rights. A libertarian would say that people get paid what they deserve when everyone can freely bargain. A liberal might point out that employers have vastly superior bargaining positions. Interestingly, what liberals say about employees and bargaining is not dissimilar to what conservatives say about prostitutes: when you look at the circumstances most prostitutes find themselves in, how "voluntary" are their actions really? Libertarians perceive "voluntary action" to be extremely well defined: basically, if you did it, it must have been the product of your totally free exercise of will. Both liberals and conservatives take more nuanced views (though in different contexts).