MMU
The MMU is a component of many computers that handles memory translation, memory protection, and other purposes specific to each architecture. This article is meant to be a generic overview of the MMU. For specifics to the x86 please check Paging or Segmentation.
Translation
The MMU's main service to the computer is memory translation. Memory translation is a process by which virtual addresses are converted to physical addresses. We can say that the virtual addresses are mapped to the physical address. This gives us the ability to create a memory model in our own fashion. That is, we can rearrange how the memory seems to be ordered.
For instance, this technique is used when creating a Higher Half Kernel. The kernel is loaded at location x, but when paging is initialized the MMU is told to map location x to 0xC0000000. This then creates the effect that the kernel actually is at 0xC0000000.
Protection
Because we can make memory seem however we want, we can make each process appear that it is the only process on the machine. Moreover, because the process can only see memory that it has, it cannot modify or copy any other application's memory. This means that if an application is to fail, it will fail, but nothing else.