What is introspection? Nothing! Or rather, almost everything.
A long philosophical tradition, going back at least to Locke, has held that there is a distinctive faculty by means of which we know our own minds -- or at least our currently ongoing stream of conscious experience, our sensory experience, our imagery, our emotional experience and inner speech. "Reflection" or "inner sense" or introspection is, in this common view, a single type of process, yielding highly reliable (maybe even infallibly certain) knowledge of our own minds.
Critics of this approach to introspection have tended to either:
(a.) radically deny the existence of the human capacity to discover a stream of inner experience (e.g., radical behaviorism);
(b.) attribute our supposedly excellent self-knowledge of experience to some distinctive process other than introspection (e.g., expressivist or transparency approaches, on which "I think that..." is just a dongle added to a judgment about the outside world, no inward attention or scanning required); or
(c.) be pluralistic in the sense that we have one introspective mechanism to scan our beliefs, another to scan our visual experiences, another to scan our emotional experiences....
But here's another possibility: Introspective judgments arise from a range of processes that is diverse both within-case (i.e., lots of different processes feeding any one judgment) and between-case (i.e., very different sets of processes contributing to the judgment on different occasions) and yet also allows that introspective judgments arise partly through a relatively direct sensitivity to the conscious experiences that they are judgments about.
Consider an analogy: You're at a science conference or a high school science fair, quickly trying to take in a poster. You have no dedicated faculty of poster-taking-in. Rather, you deploy a variety of cognitive resources: visually appreciating the charts, listening to the presenter's explanation, simultaneously reading pieces of the poster, charitably bringing general knowledge to bear, asking questions and listening to responses both for overt content and for emotional tone.... It needn't be the same set of resources every time (you needn't even use vision: sometimes you can just listen, if you're in the mood or visually impaired). Instead, you flexibly, opportunistically use a diverse range of resources, dedicated to the question of what are the main ideas of this poster, in a way that aims to be relatively directly sensitive to the actual content of the poster.
Introspection, in my view, is like that. If I want to know what my visual experience is right now, or my emotional experience, or my auditory imagery, I engage not one cognitive process that was selected or developed primarily for the purpose of acquiring self-knowledge; rather I engage a diversity of processes that were primarily selected or developed for other purposes. I look outward at the world and think about what, given that world, it would make sense for me to be experiencing right now; but also I am attuned to the possibility that I might not be experiencing that, ready to notice clues pointing a different direction. I change and shape my experience in the very act of thinking about it, often (but not always) in a way that improves the match between my experience and my judgment about it. I have memories (short- and long-term), associations, things that it seems more natural and less natural to say, views sometimes important to my self-image about what types of experience I tend to have, either in general or under certain conditions, emotional reactions that color or guide my response, spontaneous speech impulses that I can inhibit or disinhibit. Etc. And any combination of these processes, and others besides, can swirl together to precipitate a judgment about my ongoing stream of experience.
Now the functional set-up of the mind is such that some processes' outputs are contingent upon the outputs of other processes. Pieces of the mind stay in sync with what is going on in other pieces, keep a running bead on each other, with varying degrees of directness and accuracy. And so also introspective judgments will be causally linked to a wide variety of other cognitive processes, including normally both relatively short and relatively circuitous links from the processes that give rise to the conscious experiences that the introspective judgments are judgments about. But these kinds of contingencies imply no distinctive introspective self-scanning faculty; it's just how the mind must work, if it is to be a single coherent mind, and it happens preconsciously in systems no-one thinks of as introspective, e.g., in the early visual system, as well as farther downstream.
[For further exposition of this view, with detailed examples, see my essay Introspection, What?]