ok so the story in a nutshell is - Jake is at his mom's house. He finds a popsicle stick of his dad. We have a memory of his dad's. He wakes up and is confused about whether he is Jake or his dad. We meet the neighbor. We have a memory of his brother's. In his brother's memory, maybe his brother has some of his father's memories. Jake wakes up and is confused about whether he is Jake or Jon, but less confused this time.
He finds the popsicle stick that has his brother on it (which he dropped earlier). We have a memory of his mother. In this memory, his mother seems to have some memories of his father's and of Jon's. Then he wakes up and he has made a popsicle stick of his mother.
OK, so the main idea is popsicle stick = container of person's memories. Jon makes one of David, Betty makes one of Jon, Jake makes one of Betty. They stacked up until Jake contains all their memories plus his own (presumably Roger's as well). Now Jake knows what really happened to them all.