Here's another Husserl lecture to listen to, which sets Husserl in historical context as a contemporary of Freud prior to World War Two. The unnamed lecturer (I'll be happy to update this post if someone can figure out who this is) talks a little about the relationship between Hegel's Phenomenology of Spirit and Husserl's phenomenology.
The lecturer characterizes phenomena as phenomenology understands them as inherently mental, meaning that "phenomenology of consciousness" would be redundant. As I've tried to convey, I think this characterization of phenomena, i.e. the objects of consciousness, as mental, is problematic: it's entirely the point that consciousness is what puts the mind in contact with things that are not mental, or more precisely, "the mental" is not rightly understood according to Husserl as a distinct sphere from the rest of the world; consciousness is inherently an openness to the world, not a parade of representations that somehow reflect (or fail to reflect) the world. However, the lecturer then goes on to describe Husserl as participating in the tradition of folks who tried to banish Cartesian dualism, which suggests the point I've just made.
In a somewhat confusing part where he describes a sit-com, he discusses the technical term "intentionality," which means directedness towards the objects of consciousness, as if it meant our ordinary definition of the word, i.e. having a plan (intention) to do something. He says that the relation of consciousness to the universe is comparable to having intentions (plans) that don't jibe with the conditions of the outside world.
It's true that the two uses of the term have a common origin, in that one of the attitudes that consciousness can be aimed at the world is through a willing act: having an intention to do something. The phenomenologist's concept of intentionality is a generalization of that to other types of consciousness, in that I can have plans regarding the world, but I can also perceive it, desire it, fear it, etc. I think the lecturer understands this, but continues to say confusing things about intentionality all the way to the end of the lecture, neglecting to mention that Husserl's notion of intentionality modified from the scholastics was the direct and extremely detailed product of one of Husserl's teachers, the psychologist Franz Brentano, for whom intentionality was not something that could be defined in a quick sentence or two but required an entire very large book to prove and elaborate.
Maybe the most useful part of this for the listener new to Husserl is in end of the second and beginning of the third part, where the lecturer goes into some detail describing what it is to "bracket" the existence of the external world as Husserl tries to do.
All in all, this is an accessible talk that works passably as an introduction to Husserl, or as in my own case as a listener, another attempt to make this difficult figure comprehensible. From the context, it's clear that this lecture is part of a larger overview covering both analytic and continental philosophy, trying to give people a basic understanding of these disparate ideas, in much the same manner as our podcast.
The second and third parts of this talk can be found here.