To do this, before going to bed, you need to put on (place in one of the three compartments of the small inventory on the left) the decoration that you receive from the furry character. This should happen according to the plot.
But I will answer: the essence of the dream world is that there you can view your adventures again (which have already been completed. To do this, you need to try to LEAVE, but not EXIT it), and also chat with one interesting girl.