Husserl's lectures on passive synthesis (which is what everybody calls them) were actually entitled Lectures on Transcendental Logic. What he's trying to get at in them is the source of meaning and truth. Big time stuff.
What I was reading today included a remarkable section on the paradox Husserl saw at the heart of knowledge of all kinds, but especially scientific knowledge. He says that we accept, as the regulatory norm of knowledge, a logic of truth (I'll call it; I'm being freer with language rather than stick to technical terms). That is, we accept that something is known truly when we can provide evidence of its intuitive meaning and logically connect the evidence to the judgment we make. For instance, the knowledge judgment that "the pencil my sister made for me is sitting on my table" would be truly known iff I have evidence of its truth and can demonstrate the logical validity of the judgment I've made (that is, that the evidence is evidence of the truth of the judgment).
Our judgments, and the logic of truth implicit in those judgments, is never met with perfect evidence, in part because every act of perception aimed at some object is incomplete and incomplete specifically as presenting evidence. Whenever I look at the pencil, I do so from some angle, which is to say that I never see the whole pencil. Even a series of looks at the pencil exhaustive of all possible angles (which of course is not something I could actually achieve) is not exhaustive or final seeing of the pencil, because the series has to be held together for consciousness by way of retained experiences - that is, by merely figural intentions of the pencil that are not filled in with evidence. The glance I had from the front is not the perspective I have now, and all I have is the trace of that glance, not the full evidence of that perspective. Furthermore, the traces themselves are held together in that series of glances "passively," by perception itself, as it were, since we're just not capable of holding them all actively in consciousness at once.
In short, our judgments always exceed their warrant in perceptual evidence, and the logic of truth that binds them together itself lacks direct evidence, because of the passivity of the series of retained evidence. Husserl puts it in hyperbolic terms: there's nothing to say that the series of evidences couldn't just run right off the rails at any moment, and just utterly fail to continue to provide concordant ratifications of the series. After all, we sometimes make errors in our perceptual judgments, and we experience those errors just that way: the series stops continuing.
So when I make the judgment that "the pencil my sister made for me is sitting on my table," my consciousness writes a check my perceptions can't cash. This is essential to every external perception and every judgment about matters of fact in the external world. That could be a recap of Hume's skepticism, except for the turn Husserl makes, which is to say that, despite all that, we really do know. The question isn't whether or not we know, the question is, how is it that there came to be something to know, for a critter whose perceptions are always incompletely evidentiary, inchoate, dependent?
One of the pleasures of philosophy is to be able to sit down with a thought like that and let the weirdness of it wash over you. Husserl's not everybody's cup of joe, I realize, but for my money, he gives good weirdness.