It is "Saint-Saëns, Camille Introduction + Rondo Capriccioso". It was also used in Episode 4, when Kousei and Kaori perform together for the first time.
I believe the segment we hear here begins around the time that Kaori starts playing the violin again after stopping for Kousei. If you remember, she encouraged him to start again. We hear a lot of Kaori's and Kousei's thoughts during this time, where she wants to join him in the journey to being a musician. To struggle together no matter how dark the road ahead is. She is most likely trying to bring back Kousei's memory of the struggle they faced together on that stage, and encourage him again to continue.
Here is a version of it on YouTube.