The context: In the video the narrator is telling us about Aristotle's Poetics and the advice it contains for authors of tragedies:
make sure to use: peripeteia - a change in fortune, when for the hero things go from great to awful [in Titanic, Leonardo de Caprio gets Kate Winslow (great) then they hit the iceberg (awful)] and anagnorisis - a moment of dramatic revelation when suddenly the hero works out their life is a catastrophe.
A revelation is when a character discovers or reveals something, and a dramatic revelation is when this is surprising to the character or to the audience.
The speaker tells you that anagnorisis is a particular type of dramatic revelation that is used in Greek Tragedy.
In particular, it is when a character discovers the truth about how terrible everything is.
If you know Greek plays, you will know Oedipus Rex. In this play, Oedipus kills a man and has sex with a woman. Then he discovers (or "works out"):
The man is his own father and the woman is his own mother!
That is a dramatic revelation when suddenly the hero discovers that their life is a catastrophe.
There is another example in the pictures you see in the video.
Your quote is a fragment. The full sentence would be:
Make sure to use anagnorisis — a moment of dramatic revelation when suddenly the hero works out their life is a catastrophe.
This is imperative "Make sure to use..." and the part after the dash is the definition of anagnorisis. The definition is a structured as a noun phrase "A moment of dramatic revelation" which is modified by the "when" clause "when suddenly the hero works out ...". And "To work out something" means to finally understand something.
