Okay. The page file is used as "virtual memory." (A real computer term.)
Each process that runs under the NT kernel is given a 4 gigabyte address space. Normally, the upper 2 gigabytes are reserved for the OS to use, and the app can use the lower 2 gigabytes.
Each process has it's own private 2gb space that other processes can't see.
Now, of course, you don't have 2gb of physical RAM for each process, and each process isn't going to use the full 2gb. The operating system keeps track of how much memory each process is using, and where in physical memory is mapped to where in each process' virtual address space.
Memory that a process is accessing needs to be in physical RAM. But memory that's not being used at the moment can be swapped out to disk. This is what the pagefile is for. The memory manager keeps track of memory usage and swaps pages out to disk to make room in physical RAM for pages that need to be accessed by running apps.
Under the i386 architecture, pages are 4K in size.
Before you wonder if you can go without a pagefile, don't. The memory manager needs a pagefile, for reasons that neither you nor I fully understand. The NT memory manager is quite mature and has been written and tweaked by some very, very smart people, and I'm not about to try to second-guess them.
For the real gritty, low level details of the memory manager, see "Inside Windows 2000, Third Edition" by Solomon and Russinovich.