Muggles' Guide to Harry Potter/Places/Platform 9 and Three Quarters
|Muggles' Guide to Harry Potter - Place|
|Location||Kings Cross Station, London, England|
|First Appearance||Harry Potter and the Philosopher's Stone|
General Overview 
Platform Nine and Three Quarters is a secret platform at King's Cross Station in London. From this location students for Hogwarts are able to catch the Hogwarts Express train. This train runs directly to Hogsmeade Station, close by the school.
Extended Description 
Platform Nine and Three Quarters is reached by leaning against, or running through, the barrier between platforms 9 and 10 at King's Cross Station. It is apparently physically located within the confines of the station, though perhaps at a lower level, as the train does seem to pass through an appropriate area of London as it leaves the city. Leaving the platform is generally done by walking through an archway, and a wizard railway guard allows only a few students through at a time to prevent alarming the Muggles when a large number of students appear through a solid brick wall.
The platform has been used in the third, fourth, fifth, and sixth year, as the place for last-minute questions and warnings, as Harry, Ron, and Hermione depart the place they have been through the summer for another year at Hogwarts. In the first year, of course, it was the stage for the initial meeting between the Weasley children then attending Hogwarts (Ron, Fred, George, and Percy), and Harry; it proved inaccessible in the second year due to the well-intentioned but misguided actions of Dobby the house-elf; and as Harry did not attend school in his seventh year, we never reached this platform.
While the platform might well have been intended to be the place where we change from Muggle to magical life, it has only actually acted as that transition once, in Harry Potter and the Philosopher's Stone. In the other four books where it is a factor, and in Harry Potter and the Chamber of Secrets where it is inaccessible, Harry has been living in the magical world for at least a short time before the trip to the station: three times at The Burrow, once at the Leaky Cauldron in Diagon Alley, and once at Number Twelve, Grimmauld Place.
That is not to say that it is not a transition; in each case, it is a return to school, and thus to a place where Harry's own use of magic is not only permitted, but required. Harry, as an underage wizard, is of course not allowed to use magic anywhere except school. It seems that the largely unsupervised Hogwarts Express is seen as an extension of school, for the purposes of determining whether magic is allowed. Thus, the transition from the repressed world of the underage wizard, to the free world of the wizard who is able to cast spells, seems to happen on the platform.
The reverse transition, of course, happens in the other direction. Stepping off the train and onto Platform Nine and Three Quarters is a return to the world of the underage wizard, a return to the world where magic must be repressed or hidden for fear of frightening the Muggles. We see, in each of the first five books, Harry's reluctance to approach that transition, to return to the unexciting life he perforce must share with the Dursleys.
There is some question, of course, as to why so many students travel on the Express. London is in the south of mainland Britain, and Hogwarts is in the north. Would it not make sense for students who live further to the north, like Seamus Finnigan, who is apparently Irish (although we don't know where he lives over the summer), to travel directly to Hogwarts, rather than detouring far to the south of Britain to London and then heading further north to Scotland? This question is never addressed, though it may be worth pointing out that a lot of the British rail network is what is called a "hub and spoke" topology. For reasons dating back to the early days of the railroads, it seems that almost all railroads run to or from one of the several London stations, with relatively few interconnections. It may be simpler to connect with the Express in London than to try and find a train that runs in a more direct manner, particularly since Hogsmeade, as an all-magical village, likely does not appear on many rail schedules.
It is mentioned on the Pottermore web site that travel on the Hogwarts Express has been mandated by Wizarding law, in order to prevent mass migration of students at the start and end of the school year, and use of more dangerous means of transportation. No suggestion is made as to why mass migration to London at the same times is considered less alarming to the Muggles.
Greater Picture 
In the seventh and final book, of course, Harry does not attend school, and so the transition from Muggle to Wizarding worlds does not occur. However, in the opening chapters of that book, Harry reaches his seventeenth birthday and comes of age. At this point, he is allowed to do magic on his own, and so the transition from repression to encouragement of magic does not require boarding the Hogwarts Express. As he has also left the Dursley house for the last time, there have already been fairly major transitions, so adding another one would be superfluous.