Let me start by saying that this is a very simplified explanation, not the definite guide to virtual memory;
Virtual memory basically gives your process the illusion that it's the only thing running in the memory space of the computer. When the process accesses a virtual memory page, the MMU translates it into a physical memory access. If the physical memory page does not yet exist (or isn't in physical memory), the process is suspended and the operating system is notified and can add the page to memory (for example by fetching it from disk) before resuming the process again.
One reason for virtual memory is that the process doesn't have to worry too much how much memory it uses and doesn't have to change if you for example expand physical memory on the machine, it can just work as if it had all the memory it can address and have the operating system solve how the actual memory is used.
The reason it doesn't (usually) slow the computer to a crawl is that many processes don't use big parts of their memory at all times, if a memory page isn't accessed in an hour, the physical memory can be put to much better use during that hour than to be kept active. Of course, the more memory your processes actively use continuously, the slower your process will appear to run.
