This answer has been mostly rewritten to reorganise the structure and make the message clearer. I have also opened it as a community wiki answer; Feel free to edit.
Paging is a memory management scheme through which fixed-size blocks of memory have processes assigned to them. When memory usage rises to a high level (i.e. 80% capacity), paging begins to extend from RAM into vRAM (virtual RAM).
vRAM is located in system storage, usually within a hard drive, or other sizable storage locations.
Processes are assigned part of your hard drive to run as memory and will treat their section as RAM. This is a perfectly normal process, however, when the time spent to transfer data to and from the vRAM increases, system performance decreases.
While dedicated RAM is accessed directly through the motherboard from the CPU, which provides a fast connection, virtual RAM must transverse cabling between the board and the location of the vRAM.
This however, causes only slight performance impact. When the rate of which paging to vRAM takes place increases drastically (when dedicated RAM approaches capacity), thrashing takes place.
Thrashing is the practice of quickly and rapidly transferring pages of memory into your virtual memory. This takes a huge toll on performance as more time has to be spent fetching and addressing data.
Lets say, you want to write down a number 30 digits long. You could either sit next to your screen with your notepad and write it (using the dedicated memory), or you remember chunks of 5, run into the next room and write it down on your notepad in there (using virtual memory). Both get the job done, but which is going to be quicker?
Find out more about thashing here!
A big thanks to the contributors of this answer including Daniel B, xenoid and Jon Bentley.