The reason Montessori classrooms are filled with multi-aged children and are separated by three year age groupings is because Dr. Montessori said there were four planes of human development; concrete (0-6 years old), cosmic (6-12 years old), cultural (12-18 years old) and constructive (18-24 years old).
What this means for classroom settings is that children are separated by planes, and then separated once more into sub-groups. The first group includes infants and toddlers, then 3-6 year olds (which is the age I teach), then lower elementary or 6-9 year olds, then upper elementary or 9-12 year olds, and so on. From the ages of 0-6 children are in the Concrete plane and have an "absorbent mind". From 0-3 children are in the stage of the "unconscious mind" or things they won't remember and from 3-6 they're in the stage of the conscious mind or things they might (or will) remember.
Children from 0-3 years old are moved around in their environment. They don't have a choice. They are moved from someone's arms, to various swings and bouncers and playpens, to car seats, to strollers, to someone's arms, etc., etc., etc. Once they can move they're typically put "in" something so that parents can get things done or for safety reasons but they're still absorbing intelligence unconsciously. 3-6 year olds can't be constrained in strollers or playpens. It's harder to keep them occupied. They touch everything, and they want everything. They are absorbing intelligence consciously through their own actions. Montessori said "the hand is now an instrument of the brain" -- meaning by touching things the child gains experiences and develops. Their sole purpose is to gain independence and they want to do things themselves. "Help me do it myself" is sort of a Montessori tagline for children of any age but specifically for 3-6 year olds.
Their developmental objective is to acquire the fundamental abilities that lead to the development of a whole person. Pretty intense for someone just born, huh? At this age children are in their sensitive periods for sensorial mastery and exploration, effortless acquisition of language, and order and process. A sensitive period refers to the time in a child's life when they are at their greatest readiness to acquire a skill. This is not to say that if they don't learn something during their "sensitive period" they'll never learn it. Just that it'll never be as easy to do so. That's why it's so easy for young children to learn multiple languages but harder for adults to do the same thing.
The book The Absorbent Mind is a hard read. It's a fascinating book but at times scientific. I've read it a few times now and I get something different out of it each time. It's the "bible" to Montessorians. Many parents have said that it has totally changed how they look at their kids and how they plan to raise them going forward. I'd recommend it if you have time to spare and you're able to focus. You may want to have a highlighter in hand because most likely you'll want to mark up some of the pages.