If you don't get the point of the story, the entire storyline is the visit from the Psychologist. The "challenges" are pictures and objects shown to him by the Psychologist which he has to explain what it feels like and means. He's explaining to the Psychologist that it's like how his life used to be except that he's doing it all by himself instead of with Kathryn. He then goes on to explain about what happened with Kathryn, but it's unsure of how she died, probably with a challenge they did together. The green box at the end of every challenge signifies the box that he had to find to put her into. The flowers that you spawn at/checkpoint are the 2 flowers he put next to her grave. Personally, I think she died a normal death, and he just put her in the box and buried her because he couldn't handle her death. But that's just me.
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