They represent different stages in her young life, and mileposts for her to attach memories to. She reflects on houses that were dirty, or uncomfortable, or in dangerous neighborhoods. She writes of leaving in the middle of the night when they couldn't make rent.
Her dream house is one that is clean, and big enough, and safe. Something she could proudly show her friends or her teacher.
This gets more realistic as the stories progress. She matures to realize she may never see her dream house, and that the one they live in is not as bad as she thought. She realizes it's more about the family in the house.