I can't say I've ever heard of that term before. Using the handy Dictionary.com, here is my guess -
Libertarian is the belief in free will. Its opposite is "necessatarian" which means "Of or pertaining to the doctrine of philosophical necessity in regard to the origin and existence of things, especially as applied to the actings or choices of the will; -- opposed to libertarian." http://dictionary.reference.com/search?q=necessitarian
Libertarian free will would therefore be a sort of "uncaused effect". It has been debated (and rightly shown) that free will is a misnomer precisely because there are causal factors that impact decisions we make. In the case of the Open Theists, I think the book would be pointing out that they do not believe that even God can impact our free will. In order for our decisions to be of value, God cannot have a hand as a causal agent in our will - this includes, but is not limited to, his knowledge of the future.
It's a stumbling attempt to answer your question. I'm sure there are others on this board who can answer your question better.
"Free Will" says that we do whatever we want.
The Calvinist undestands that as a sinner what we want is always sin! So we are free to do what we want, but cannot change the wanting of it. That is why we must be regenerate, given a new heart, called from death to life by the Holy Spirit so that He can give us new desires!
"Libertine/Libertarian Free Will" says that we do whatever we want and that we are in control of and can influence what we want. We can decide what to desire. So instead of total depravity and inability, we are able to choose to do right and can, of our own volition, change our desires so that we want to be saved.
Libertarian Free Will is a will that is completely free of any and all influence or coercion outside itself. Besides the fact that it is unbiblical, the concept itself is quite silly. A will that is free in the libertarian sense could never make a choice because every available option would be equally desireable and undesireable at the same time, and thus the will would never choose anything.