The definition of 'understand' by mathematicians is quite different from how we use the word in everyday conversation.

If you "understand" a concept, you need to be able to answer the question of why the concept is correct. "It is written in the book" is not a proper answer. You need to explain it in your own words. If the book uses a theorem or definition that you do not know, you must investigate it.

Yasuyuki Kawahigashi prohibits to see notes at the seminar. He defines "understand" as the state which you can explain the concept with your own words without seeing anything.