Does this explain it for you, or are you looking for something more detailed?
Barbour is speculating that if we solve the Wheeler-DeWitt equation, we’ll get a single probability distribution over the configuration space of the universe, and all of our experiences can be explained using this distribution alone. Specifically, we don’t need a probability distribution for each instant of time, like in standard QM.
Does this explain it for you, or are you looking for something more detailed?