This memory appears twice in the film, once for Riley's mother and in the end, for Riley's teacher when she was craving for summer. The image of the memory for reference:

So, was this supposed to be a reference to any character from a previous (or upcoming) pixar movie or any other animated movie?

Or does this memory have a story behind it? Or some canon explanation from the directors?

The wiki isn't really clear on it. It claims that it was supposed to be a memory of Riley's mother when that guy have proposed her. If that is right, then why does the teacher have the same exact memory?