At the risk of sounding like a complete buffon;
It's almost like the simplicity, and the clean simple depiction of the painting excavates deep seated memories from my life into the the scene. Four people, seated closely, yet they appear to be strangers. There is one waiter, and 3 people who's relationships are ambiguous. The area outside is dark, but not cold, yet the inside emits a type of warmth that you can almost feel, as the light spills out slightly onto the concrete outside. I see the diner as an island in this sense, and the view we have of the diner could almost be from somebody crossing the street. If you notice, the glass is almost not even there on the diner, as if it was see through. We do not see the door into the diner in the painting, which adds to a certain level of mystery.
Honestly, I think I've gone enough into detail, and I'm still not scratching the surface. It just resonates with me. And I feel that a lot of the best artwork and those that we love just captures an emotion that we can't put a finger on, and that's what makes it special.