In the not too distant future we are going to find out at the same time Peter will that he is not the Peter he believes he is. I would love to pretend how brilliant I am in figuring this out but the credit has to go to rosie77 for this post: "but hey, think about it, if u were Peter, would u be mad? I would be, I mean here I am thinking all this time that I am who I am an then I find out I really died a long time ago, and u took the young me from an alternate world? hmmm, shit is gonna hit the fan."

We are going to find that the real Peter and Walters son died as a small child as rosie said and his bad dreams had to do with being kidnapped and being relocated into this dimension. What confirmed it for me was in this episode when Walter said about Peter after he was abducted "I can lose him again."
Good call rosie77, nice job.
What it means is Peter is not Walters son.