Relative to the purchasing options, it's free insofar as the marginal cost is zero.
Yes, technically someone - whether a donor or taxpayers - had to buy the book, construct the building, fund ongoing operations, and so on. But any of your tax money that you might have paid for this is a sunk cost - there's no additional user fee you pay in order to take out Seven Habits (or any other book).
Such a library is considered private, although such libraries may have public access. Public libraries are considered public by virtue of being publicly funded, partially or wholly, via taxes.
It's not free.
It's a copy that you and others in your area had purchased for you, by your local library, with money collected through the tax mechanism.