Namespaces are the wiki's individual partitions. Explaining them is a bit difficult abstractly- the concept is simple enough provided you can actually see and play around with it. First, go to a TV Tropes page. Examine the exact web address (the part that begins with "http"). Somewhere in that line should be the word "Main". If you don't see it, just keep clicking "random page" until you find one that does. The word "Main" (or any other word located in its place in the address) represents that page's namespace. Mainspace is the default namespace. If you write a Wiki Word on any page (usually by rewriting it as WikiWord), the page linked to is in the mainspace. If you write a Wiki Word for a page that does not exist, then you are directed to an empty page with the message "Describe Wiki Word here". At least, that's what it used to say- this message has been changed over the years because tropers would simply leave "Describe Wiki Word" and begin by saying such things as "oh, where to begin?"
The original intent behind namespaces was actually simple subdivision. The original alternate namespaces were simply titles like "Anime", or "Film", or "Series". The idea was that when making a trope page for a show (as opposed to a trope), the page would be written in the namespace for whatever media form the show was originally designed in. An example of this would be VideoGames/StreetFighter This did not catch on, since people just used the basic WikiWord format for creating pages. This is understandable when you consider how little new users know about actual page formatting- I must have been on the site at least a year before I figured out how to create alternate Wiki Word links. This ignorance was not a significant hindrance when I created new pages or modified old ones, which says a lot as I was a fairly heavy user.
After the original intent fell through, namespaces were adapted to simply distinguish between works which had similar titles. Street Fighter, for example, is a video game series at heart, and that is its mainspace page. Pages for this series also exist in the Anime, Comic Book, and Film, namespaces that are about those specific series. This worked reasonably well, with the main snag being tropes which were named directly after works of media. There is no Trope namespace because all tropes are presumed to exist in the mainspace- the original plan, you may recall, was that shows wouldn't be in the mainspace at all. An admin fiat eventually clarified this dispute by simply banning any trope names that were identical to the names of works of fiction. A good move since, all things considered, such names were rather lousy.
From there, namespaces evolved into a communication of ideas based on simple prompts. It Just Bugs Me and Wild Mass Guessing are the most popular namespaces, and take the form of direct theories and conversations about shows. ItJustBugsMe/StreetFighter, for example, is about parts of the greater Street Fighter universe which do not make sense. Because of the way namespace is shared, It Just Bugs Me pages for series like Street Fighter tend to be much larger and disjointed, as by design they must cover every single iteration of the broader Street Fighter series. Pages for specific games and works of media regarding Street Fighter fortunately take off some of the slack in that they have their own It Just Bugs Me pages. Or at least could, provided that somebody makes them by manually typing the namespace into html address.
Later on, as some trope pages reached critical mass, the point at which example listings become so long as to become impossible to read, these were given their own namespaces. One example of this is Memetic Mutation. Very obviously a trope, and not an opinion, discussion, or alternate version of the work in question. Be that as it may, if you go to MemeticMutation/StreetFighter, you will find a listing of Memetic Mutation examples related to Street Fighter. Bear in mind that with Street Fighter, it has its own page because there's a great deal of Memetic Mutation about Street Fighter specifically. Most generic Video Games are instead listed, somewhat confusingly, as MemeticMutation/VideoGames- at least until or unless the game in question has so much Memetic Mutation added to it that it earns its own page.
Discussion pages were also a form of namespace at this time. However, they were not created via WikiWord but rather by pressing the blue "discuss" bubble at the top of the screen, and so were seldom thought of in the manner here described, though the formatting was identical to that of any other page on the wiki. Eventually the discussion namespace was replaced altogether with a discussion-style software system, which persists to this day.
The namespace idea is a tool that has gained much broad, improvisational use throughout the wiki as way to more effectively split pages and make them readable. This was not foreseen by the site's admins, but they never really anticipated that it would become this popular to begin with, so it's quite understandable that this plan along with many others had to be jettisoned when it became clear that casual users of the wiki were improvising their own solutions to problems. It's one of the more technical aspects of the wiki that really makes plenty of sense once explained- but older users often failed to do so because we kept forgetting that not everyone intrinsically understands how the system works. So, sorry for not writing this earlier.