One thing I really liked about that sequence is it was Luke finally being able to re-emerge. This whole time, he was crushed by this burden of what he felt he needed to be for the galaxy, and for Rey. In Rey's case, he felt he needed to convince her that she shouldn't pursue being a Jedi, so he very forcefully adopts this posture of authority and conviction. It's similar to other masters such as Yoda who knew what they wanted to pass on, and were mysterious as needed to allow the pupil to go on the journey. In front of Rey, Luke can't be a guy that admits he has no clue. It weighs him down, unnecessarily.
In front of Yoda, though, this changes. It's probably the first time in ages he has ever been allowed to be vulnerable and human to anyone else. When Yoda first finds him, he's worked up and about to torch the place. Yoda dares him to do it, and Luke is like, "yeah? I'll really do it. You don't believe me?" ... but he hesitates, as Yoda knew he would, because his convictions aren't nearly as strong as he tries to let on. When Yoda torches the tree himself, this is what really crumbles Luke's facade. Gone is his brave front as he runs towards the tree in a panic, shrieking "....but the sacred Jedi texts!" in anguish. The same texts he has spent the film up to that point convincing the audience, and himself, that he'd be glad to be rid of. I love that Yoda points out that Luke hasn't even read them, so what is he even doing?
It's a really touching moment -- Luke and Yoda, pupil and master again, reflecting on the fate of the galaxy, Yoda thwomping him on the nose when he doesn't get it. It's the one chance Luke gets to chat with someone who isn't looking to him for salvation, and the burden visibly lifts from his shoulders. He becomes recognizable again as the fresh-faced boy from Tatooine in this moment, and we see that there's a lot of Luke that never really left, in spite of all he's gone through. And it sets up his marvelous final act.
Luke lost his way, but finds it again in the end, with a little help from his friends.
(Love this depiction of Yoda, by the way. It didn't even occur to me that it was the OT version of Yoda, not the prequels one, until Redux pointed it out here. Definitely like this one better, but the prequels version fit the story they were telling there, I suppose)