Kids on the Slope is an anime that's about two things: jazz music and friendship. In one scene, the series captures overcoming differences in a friendship through the power of music or more specifically, jazz music.
Before the scene above our two main characters Sentaro (the drummer) and Kaoru (the pianist) are not on speaking terms after Kaoru feels like he's been betrayed by Sentaro. During their school's recital something happens to the band that is supposed to play next and Kaoru volunteers to keep the crowd busy while the band gets everything together.
There's something you should know about Kaoru, he's kind of a nerd. At the start of the series, he doesn't really have any friends, he's constantly getting bullied, and he's practicing classical piano pieces. That is, until he meets Sentaro, who -- for lack of a better term -- is kind of a bad boy. Sentaro doesn't go to class, he only plays the drums, and is constantly getting into fights.
So when Sentaro steps on the stage to accompany Kaoru, it comes off as a big gesture. You can even see the surprise on Kaoru's face once he hears the drums start playing.
As the song goes on, you can see their differences and anger towards each other disappear. The friendship they've made throughout the series up to this point takes the forefront. Jazz becomes their way of arguing with each other. There are moments throughout the medley where one musician stops playing and the other keeps going as if to say, "okay, I'm going to listen to your side of the story, now".
The magical thing to me about this scene is how jazz -- or music in general -- is used as a tool to get through certain hardships. Through the way they play their instruments, we can see our characters have a discussion, get through their differences, and then remember what it's like to have fun with each other.