I'll start by saying that I have the AMI Montessori training for birth to age 6, and no experience with other education methods except for some volunteer work in traditional preschools, so if you see anything incorrect about another method please correct me promptly. I have done some reading but not everything on the internet is accurate – and some of the things I've read about Montessori make me cringe. With that said...
I think something that makes Montessori unique is that it is reality based. Young children (under six – what we call the first plane of development) are still trying to figure out what the world is like. If we offer them fantasy, fun as it is, that can really confuse them because they don't have enough knowledge about the world to understand the difference between reality and fantasy. So, in a Montessori environment, we offer only reality based materials for those first six years. This is one of the major differences between Montessori and Waldorf, because my understanding is that Waldorf education focuses on fantasy play as a major learning tool.
Something else that I think is unique about Montessori is that the materials were developed scientifically. What I mean by that is that Montessori didn't base her work on expectations of what the children would be interested in or capable of. She just offered a room full of materials, including toys, practical activities such as for cleaning, educational materials, and so on. Then she observed the children, and kept only the things which interested them. She added materials based on what she observed, to delve deeper into ideas that the children found interesting and to help the children develop skills that were lacking for the work they wanted to do. For example, she noted that some children were having trouble sewing, so she offered a bead stringing work as a preliminary activity to practice the motions with less difficulty. By the time the children grew bored with bead stringing, their hands were ready for the more delicate work of sewing.
The progression of materials also helps children to categorize things and understand how concepts fit together. As young as the toddler community you will see children begin to abstract the essential characteristics of things, such as, “all butterflies have wings, but not all butterflies are blue.”
Montessori doesn't assume that something is too difficult for a child simply based on age. When Dr Montessori was developing those materials, she regularly found that the children she offered them to were not interested, but children a few years younger were enamored. A big example of this is reading. When I see people saying that 5 is too young to focus on reading, I cringe a little – because if children have the opportunity to learn the sounds and shapes of the letters when they are three, they spontaneously write around 4 (with chalk or moveable letters, not necessarily pencils) and read around 4.5. The Montessori method agrees with the idea that we shouldn't be pushing reading, but emphatically disagrees that 5 is too young.
Montessori education includes work appropriate to the child's sensitive periods. In neuroscience these are called “windows of opportunity”, and what it means is that the child's brain is focused more intently on specific acquisitions at specific times. For example, when a child is in the sensitive period for developing the use of his senses (seeing, hearing, tasting, smelling, and touching), there are many materials for practicing them such as the smelling jars, tasting bottles, bells, etc. I don't know of any other educational method that includes all of those sensory experiences daily, especially categorized in so logical a way.
Montessori classrooms have mixed age groups. This allows younger children to observe older children's work and behavior, and simultaneously allows older children to experience leadership positions and be genuinely helpful. It also decreases competition for the same materials and lets younger children look forward to the materials they will be ready to work with later. I know this is rare in traditional schools, but I have no idea about other paradigms.
I also think the Montessori take on repetition is a little different. Tradition education is a huge proponent of repetition, but they do it the form of worksheets or homework, i.e., forced repetition. Montessori advocates for repetition, but only when the child is choosing it voluntarily. When a child chooses to repeat something it is because he is learning from it, and we want him to develop that concentration so he can figure out whatever it is he is trying to figure out.
This directly relates to sharing and taking turns, by the way – in a Montessori environment a child works with a material as long as he wants and returns it to the shelf when he is finished, ready for the next person. He doesn't have to share it because we don't want to interrupt his work. At the beginning many children need help with waiting for something to be available, which has the benefit of developing patience and generosity. This is because when they share, it is a volunteered sharing that is internally motivated. There is only one of each material in the environment, so sometimes a child gets a lot of practice being patient.
What Montessori has in common with some other methods is the practice of following the child's interests. I know that RIE focuses on this as well, and that both methods emphasize observation of the child, but I think Montessori takes the lead here because it offers opportunities that RIE practitioners might assume children aren't ready for or won't be interested in. For example, I've seen RIE websites advocate for later toilet learning, whereas Montessori provides a lot of precursors and makes toilets available at a young age, so that the child can mimic his elders as soon as he becomes ready without having to wait for subtle external signals (which may not come for a long time if the child hasn't had those precursors such as watching others use a toilet and feeling wetness in cloth diapers and underwear). So we offer activities by giving a lesson, and if the child isn't interested that's fine. He may be interested later and we will give the lesson again if necessary.
Montessori also shares a deep respect for the child and his inner process with other methods. The primary classroom for ages 3-6 is called the “casa de bambini”, which means the “children's house”. Montessori teachers, or “guides” as we usually call ourselves, are taught as part of our training that the materials belong to the children and not us (no matter who pays for them)... so if a beautiful material gets broken we will share in the child's sadness and repair or replace it, but we won't be angry because it was for the children, and it provided a learning experience (which is why we intentionally use materials that are breakable and require taking care). The children learn to care for their “home” and do so willingly because it is theirs and they take pride in it. They love it because it is full of beautiful things prepared just for them, and they respect it because their efforts maintain it.
There are a ton of other things that I could say about Montessori, and you can probably tell that I'm quite passionate about it, but this post is getting pretty long so I'll cap it here and answer any questions either in the comment section or a new post.
Next up is what to look for in a Montessori school!