I cannot speak in detail about the Montessori method (not a big fan of it myself) but I can give you some more detail on the misconception of self-directed play or free-play as it is often called.
The reason that it is so important in early childhood is of we want children who can think for themselves, are independent, critical thinkers we have to encourage children to make their own choices. If they get to experiment with thinking, ideas and concepts, to use trial and error and be constantly 'actively learning' they are building vital personal skills. Children are not empty vessels waiting to be filled with knowledge.
The ideal scenario is to create self motivated learners- who feel confident and interested to learn about anything and everything. Most people do not thrive in a passive learning (sit still and listen) Most prefer to touch, feel and try. So a fun and relaxed environment where they can "play" makes it safe to learn.
The key for the adults, is to carefully observe and plan the environment, and act as a resource within that environment.
So it might seem that the adults are standing back letting the children do what they like. What might not be obvious is that (in a good nursery) the adults are scaffolding the learning. They may have observed that a child only ever plays with cars, but very rarely ever draws/writes.
So on day one they might set up the cars and the road map carpet. To observe how the child uses them in his play (does he involve others? Does he use language? Does he repeat movements? Use only limited items? A lot can be learnt from even 2-5 minutes of observation.
Day two they might set up the cars and some some paint and paper.- Will this child follow his favourite item to other areas of play (If yes- this opens up a world of scope, if no- back to the drawing board!)
If successful -Day three they might set up the cars, large sheets of paper, pencils, small blocks and examples of road maps & signs. They might sit near by and occasionally say "hmmm I wonder which road I take to get from my house here to nursery." I remember there is a big bendy corner- how would I make show that on my paper?...
Constantly observing and following the child's lead, but planning the equipment & their interaction to extend and support different aspects of the child's development and learning. Often this is the first step for car-mad boys to becoming confident writers. They have the initial sense of achievement and interest some place familiar, then carry that skill to other areas of play.
Because children are developing so many different types of skills at once, to achieve deep level learning they need the opportunity to revisit resources and experiences, so they can test & retest their theories. Consolidating what they are learning. The adults role is to observe, plan and evaluate.
Hopefully someone else can expand on how this works more specifically in a Montessori approach.