For the underlying story, see here:
“When I left the United States Senate, I became a professor at the University of Pennsylvania,” Biden said. “And I’ve spent a lot of time—and the University of Delaware has the Biden School as well, so I’ve spent a lot of time on campus with college students.”
Apparently Biden was given the title of Benjamin Franklin Presidential Practice Professor at Penn (in 2017, after the end of his Vice-Presidency), which involved him giving four speeches a year, for $390,000/year, according to PhillyMag (David Murrell).
For the underlying source of the quote, you young whippersnappers who don’t know the great lines of my youth, see here.