Arya had really tough destiny - she lost both her parents, father was executed in front of her, mother was murdered. So she went across the ocean almost to another world in order to find a man with the help of whom she'd be able to avenge.
The man was a "faceless man" who taught her the art of killing and disguise. She became his apprentice and the goal of learning was to be able to take the appearance of any person.
But Arya had her own goal too - that was revenge. She was studying hard and from time to time was tested on lying. Another woman who was master's helper asked questions and beat Arya if she'd lied. They wanted her to become "no one", lose her personality and identity. - Who are you? - No one. Hit in the face. - Who were you before you came here? - Arya Stark. - Tell me about Arya Stark. And so on.. and more hitting if lying.
Finally Arya succeed in her learning, she wasn't being beaten any more when checked, changed faces and killed important people. She thought it's time to go home. The master found out it and sent the woman to kill Arya. She put a knife in Arya's belly and cut her many times, but Arya somehow survived and defeated her. She took the skin of her face and came to the master with her sword. - You ordered to kill me? - Yes. And here you are. … - Finally a girl is no one. And he was so satisfied with himself. But Arya answered.
- A girl is Arya Stark of Winterfell, and I'm going home.
For me it was a great example of critical thinking, when somebody knows his roots, what is going on and where is he heading in spite of all the obstacles and trials. She outplayed them all. And only on account of Arya and her new skill and inner determination the humanity in this Martin's universe was finally saved :)