They are trying to tell jokes.
But Del Piero allready starts laughing at the way Totti is saying his name because of his roman accent

The joke is:
Totti: Allessa, how was your test?
DP: Ah bad, bad, I delivered a blank sheet
Totti: Me too! Now the teacher will think I looked at your test!
There are some more like this one with Buffon.
Totti: I´ve found a very interesting book.
Buffon: What´s the title?
Totti: How to resolve 50% of your problems.
Buffon: Did you buy it?
Totti: Yes, I bought two!
