Arya moves on to the next phase of her training. She, partly magically, partly by literally sticking a dead person's removed face onto her face, gets a new face in the style of that bloke she helped who killed all those people for her back in Harrenhal. Jaqen H'ghar, that was him.
Anyway the rule is that to become an acolyte and get all these cool new powers and skill she's got to give up her identity and become no-one. Her heart's not really in it so I'm hoping she can fool them enough to get the cool new powers and eventually go back to being Arya, have a big Stark family reunion (what's left of them) and get revenge on whoever is still left out of GREGOR (turned into a Frankenstein's monster, presumably), Dunsen (who?), Raff the Sweetling (dead, or still hanging out with the Boltons?), Ser Ilyn Payne (off with Jaime in the Riverlands), Ser Meryn (killed by Pod in battle of the Blackwater trying to kill Tyrion, was it? No that was Mandon Moore. Meryn Trant was the kingsguard who beat up Sansa) and Queen Cersei. This level of dishonesty seems fair enough when dealing with a weird cult that turns children into assassins.
Oh yeah, because Arya has to kill an insurance guy who hasn't been paying out on claims. She does this using the poisoned coin trick seen way back in the prologue of the last book: swaps out coin by pretending to fail at robbing a sea captain. Captain pays coin to insurance guy. Insurance guy bites it to make sure it's real gold. An old trick.
That done, she's now an acolyte and is being sent off to Izembaro, wherever that is, for an apprenticeship.