This clip discusses some of the schools of thought in contemporary analytic epistemology.
First, the clip mentions Bertrand Russells dislike for the standard notion of what constitutes "knowledge" in philosophy, believing it to be to much too vague. Then there is a brief summary of G.E. Moore's "Proof of an External World" and his views on foundationalism.
The clip then mentions Ludwig Wittgenstein's idea that "meaning is use" within social contexts, and that philosophical obstacles are really just miscommunication within "language games." Simply put, Wittgenstein thought that there were no such things as genuine philosophical problems, and that philosophy was merely a byproduct of linguistic misunderstandings.
The clip then discusses the differences between foundationalism and coherentism and W.V.O. Quine's notion of the seamless "web of belief." Quine was a strong proponent of the natural sciences, and thought that findings in the natural sciences could shed significant light onto age-old philosophical questions concerning the nature of the mind and knowledge.
The clip then summarizes "The Gettier Problem" which challenged the Platonic definition of knowledge as "justified true belief," and then ends with definitions of internalism/externalism, and Alvin Goldman's causal theory of knowledge.