Now that Hello neighbor has released and I’ve beaten it, here’s my theory on what it all means.
Warning, spoilers!
[EDIT] added some more to the ending.
From my understanding, The first two acts are real, but the third is a dream.
As a kid, you see the neighbor is doing something strange, possibly trying to kill someone, and locks them in the basement. Once you get into the basement, The neighbor finds you and locks you up too. You escape the basement and then escape his house.
Later, the player, all grown up, gets evicted from his apartment and moves back to his childhood home. He sees the neighbor's house, broken down and destroyed, and his fear (The shadow man) comes back to him as he remembers when the neighbor kidnapped him.
He falls asleep, and his fear creates a sort of dream world, representing all his fears, including the neighbor. You beat the three fear rooms, conquering your fears and becoming stronger, and enter the basement again, You escape the neighbor this time, strong enough to push him away. However, your fear of the neighbor isn't fully overcome, so now you fight a giant version of him.
Once you overcome that, you are face-to-face with the embodiment of fear itself, the shadow man, tormenting your past. Gradually, you become bigger and stronger as you stand up to your fear. You finally push it away, destroying your fears. You see the neighbor in a small room. He is in one room where the door is boarded up, and on the other side is the shadow, with the exit door behind him. The exit doors represent an “exit” from your fears and leading to peace. You have overcome your fears, and now must leave the neighbor’s fears alone with him. You now wake up from your dream, back in reality and finally at peace, and move in to your old home.
As for the cutscenes you occasionally get after being caught, I’m not quite sure, but they could be the backstory of the neighbor. He lost his wife in a car crash, his daughter on a rollercoaster accident. As for the boy, I’m not entirely sure, but his cardboard cutout appears during the neighbor boss fight before he destroys the house you start in, so maybe the son was accidentally beaten to death?
