Arya is blinded by a poison she takes every day to prolong the condition. This is for training purposes. When she sleeps she telepathically links to her wolf in Westeros. Mostly she does wolf-things. It's not entirely clear to me why she doesn't use her powers to have some effect on events: possibly there is little she could do, or possibly when being a wolf she doesn't feel like doing anything other than wolf things. I suppose an assassination attempt would be risky anyway: a wolf near a large enough group of people would soon be killed. She does learn things, at least. She knows it is snowing in the riverlands (which narrrows down where her wolf can be). Also, looking back at my notes, Ser Dermont, looking for Arya's escaped uncle Blackfish, was complaining about wolf attacks, and Jaime was wondering about Arya's direwolf. Arya remembers feasting on the flesh of man, but no mention is made about whether or not this is deliberate targeting of specific men.
She makes money for the temple by dressing up as an urchin and begging around inns. She keeps up with gossip this way, too. We learn that some of those wildlings who made it to Hardhome have been captured as slaves (thinking the slave ships are the promised rescue ships).
She gets a new power: she can now see through the eyes of a cat that has befriended her. It seems there has always been a connection between Arya and cats: back when she was sneaking around Winterfell there was a particular cat that never seemed far away. This seems like a very useful power.
She uses this power to figure out who it is that keeps attacking her with a stick (for training purposes). It's the kindly man. When she tells him she knows (but not how) this is enough for him to deem that her blindness training is over and she is given some other potion and wakes with her sight restored.
I have absolutely no idea what will happen next. Hopefully she will use her cat powers to some great effect.
