A pun is using a word or phrase which can have different meanings
When I was born they threw away the mold, well some of it grew back.
is a pun on "mold" being both a form from which things are made and the green furry stuff that grows on spoilt food.
A
Talmudic pun
is a pun on or in the Talmud (Judaic doctrine).
The Talmudic pun the author is referring to is here:
The Talmud in Tractate Berachot famously takes the word banayich, your children, and interprets it as bonayich, your builders, indicating that students of Torah build and preserve the Jewish people through their study.
It has been interpreted to mean that
our children become our builders
our children are our future
The author of your passage has paraphrased it to be
our students have become our builders
Both sayings point to the fact that the next generation is the future.