This was making the rounds last night.
Arya had two choices:
1. Kill the actress, which would signal her transition to No One, a faceless killer with no identity, serving the gods and killing whoever she is told to kill, regardless of who they are or what they did. This would mean giving up her kill list and murdering actresses, blacksmiths, other innocent people. Remember, Lady Crane had a contract on her head just because the younger actress wanted her position. The other option was...
2. Spare the actress, which means quitting the Faceless Men, remaining Arya Stark and returning to Westeros to exact her revenge. Remember, Jaqen had already sent her on a mission, but she killed Trant instead. He told her if she failed this time, she wouldn't get another chance.
The play was a retelling of her family history, and shows how the rest of the world views the Starks: fucking dingbats who got themselves killed. Jaqen sent her there to test her resolve and see how she would react to the people mocking her family - would she be able to let go of her name, or would she remain a Stark? Obviously she can't let go of her kill list, and she took her destiny in her own hands by leaving the Faceless Men.
No, this doesn't completely nullify her Braavos story arc. She learned how to fight blind, how to prepare bodies/skin for use in the Faceless Men's transformations, and she learned how to change her face when Jaqen sent her on the mission she bungled by killing Trant instead. She was trained.
The ultimate significance of the Braavos arc is, this was Arya's chance to free herself. She's been running away from her problems the entire series, but when she found Needle and ran from the House of Black and White, it's the first time she's truly taken control of her life and decided to operate on her terms.
>mfw I actually had to explain this to multiple people