Each folder which gets installed into the Windows during the installation has it's specific purpose to serve. And the system works as long as these default folders are functioning along with the kernel. Here's the short explanation of what each is going to be used for.
Program files : This folder holds the 3rd party applications which are 64 bit. Fore example VLC installation will go in this folder if it's 64 bit. Default Windows applications are not stored here. This folder is not invisible as it shows the applications installed and allows you to modify if you have UAC rights.
Program Files x86 : Same as Program Files but this folder stores the 3rd party applications which are 32 bit. And this folder also contains some of the default Windows applications which are not pre-installed by Windows during the installation. This directory too is not hidden.
System Volume Information : This is a hidden folder which holds the restore point data for the system. This hidden folder is specific to the partition. So C: and D: and onward each drive has this folder with specific number attached to it. The number for this folder is revision number for the restore point. It is used in cases where you want to restore the system to the functioning state.
System32 : This is one of the important folders in Windows directory. If this gets removed or even has some corruption, your windows installation ends up having various issues depending on the file that gets affected. This is visible folder. But a lot of folder inside it are not visible for protecting them from being modified or corruption. Also deleting anything inside this folder requires UAC. And lot of the files can't be deleted.
WinSXS : This folder is stored inside the Windows directory. This is the folder that grows it's size as you use the system. Depending on usage, it has temp files and cache and other things that gets stored in it. Most of the cleaner apps are using this software for removing the unwanted data from this folder.
Page file : This file holds the swap file or virtual memory data. And it helps reduce the load of swapping memory on the RAM. More the size of this file. Easier it is for the Windows to process tasks and applications to your desktop. This file is usually cleared during the shutdown. And unless specifically set, it often remains at the value assigned by the system.
As explained earlier, each folder mentioned above and few more folders make up the Windows desktop functioning along with the kernel.
The file and folder permission by default if set by Windows installer, then deleting that permission and removing those default set of files of folder means Windows can get corrupted. Some of the files and folder can be deleted using UAC access but not all files and folders can be deleted while keeping the Windows functioning.