Wants form a hierarchy. This is the key. Not all wants are on a level; some wants refer to other wants.
Simply put, we can have wants and also wants about our wants - meta-wants. For example, I can want to smoke at time t (this minute) but also want, still at time t, that at time t +1 (a future time) I will not want to smoke. I have a want (now) to smoke and a meta-want that in future I will not to want to smoke. This is the kind of phenomenon Harry Frankfurt was concerned with in 'Freedom of the Will and the Concept of a Person', Journal of Philosophy, 68, 1971, 5-10.
It this phenomenon that Schopenhauer has in mind. Freedom comes into the picture because even if our intentional actions are determined causally by our wants and desires (on the Humean model) our meta-wants can cause our other wants to weaken or disappear. Our meta-wants have the capacity to free us from our other wants.
@Canada - Area 51 Proposal. I don't think Mill's distinction between higher and lower pleasures ('Utilitarianism', c.2) comes into it. The want that I want to be rid of may be - yield - a lower pleasure; but I may well want to be rid of it - I may want-not-to-have-that-want - in order to cultivate a want for another lower pleasure, say horse-racing. I may want not to smoke in order to have more money to spend on the horses.