The master of Tyrion and Penny, Yezzan zo Qaggaz, is dying from dyssentry (it's going around the Yunkish camp). Luckily Nurse, the cruel slave handler, is dead too (surprisingly before we got to see any of his cruelty on screen). Tyrion sees an opportunity here and when the master needs water he sees his chance.
We learn that Tyrion knew about the lions but didn't tell Penny. It's unclear whether he knows it was Dany who called off the lions. He also missed the dragon, being inside a tent when all that was going on. Also Tyrion spotted Ser Barristan Selmy with Dany and almost revealed himself to him, which would have been interesting.
He goads the guards into sending him and Penny to fetch water, manages to bring Jorah Mormont along too, and after getting the water (it makes good cover for a slave with bells on his collar to walk around freely), heads straight to Brown Ben Plumm's tent. He convinces Ben that he's Tyrion Lannister, and reminds him that house Plumm is pledged to house Lannister. Have we come across any Plumm family antics before now? There's something about dragon blood running in the family: I remember the jailer at King's Landing going on about that.
It's beginning to look like Tyrion will get to meet Dany and possibly help her defend the city in spite of her husband. By being clever, by thinking of things like poisoning wells, for example, and perhaps helping with the dragon training. And even riding a dragon himself. I'm still hoping for that!