Phenomenology is the study of the structures of experience and consciousness. Literally, it is the study of “that which appears”. The first time you look at a twig sticking up out of the water, you might be curious and ask, “What forces cause things to bend when placed in water?” If you’re a curious phenomenologist, though, you’ll ask things like, “Why does that twig in water appear as though bent? Do other things appear to bend when placed in water? Do all things placed in water appear to bend to the same degree? Are there things that do not appear to bend when placed in water? Does my perception of the bending depend on the angle or direction from which I observe the twig?”
Phenomenology means breaking experience down to its more basic components, and being precise in our descriptions of what we actually observe, free of further speculation and assumption. A phenomenologist recognizes the difference between observing “a six-sided cube”, and observing the three faces, at most, from which we extrapolate the rest.
I consider phenomenology to be a central skill of rationality. The most obvious example: You’re unlikely to generate alternative hypotheses when the confirming observation and the favored hypothesis are one and the same in your experience of experience. The importance of phenomenology to rationality goes deeper than that, though. Phenomenology trains especially fine grained introspection. The more tiny and subtle are the thoughts you’re aware of, the more precise can be the control you gain over the workings of your mind, and the faster can be your cognitive reflexes.
(I do not at all mean to say that you should go read Husserl and Heidegger. Despite their apparent potential for unprecedented clarity, the phenomenologists, without exception, seem to revel in obfuscation. It’s probably not worth your time to wade through all of that nonsense. I’ve mostly read about phenomenology myself for this very reason.)
I’ve been doing some experimental phenomenology of late.