What is the difference between mapped region and unmapped region in memory space?

If memory addresses are 64 bits long, as in many modern computers, you have 18446744073709551616 possible memory addresses. (It depends on the processor architecture how many bits can actually be used, but addresses are stored using 64 bits.) That is more than 17 billion gigabytes, which is probably more memory than your computer actually has. So only some of those 17 billion gigabytes correspond to actual memory. For the rest of the addresses, the memory simply doesn't exist. There is no correspondence between the memory address and a memory location. Those addresses are, therefore, unmapped.

That is the simple explanation. In reality, it's a bit more complicated. The memory addresses of your program are not the actual memory addresses of the memory chips, the physical memory, in your computer. Instead, it is virtual memory. Each process has its own memory space, that is, its own 18446744073709551616 addresses, and the memory addresses that a process uses are translated to physical memory addresses by the computer hardware. So one process may have stored some data at memory address 4711, which is actually stored in a real physical memory chip over here, and another process may have also stored some data at memory address 4711, but that is a completely different place, stored in a real physical memory chip over there. The process-internal virtual memory addresses are translated, or mapped, to actual physical memory, but not all of them. The rest, again, are unmapped.

That is, of course, also a simplified explanation. You can use more virtual memory than the amount of physical memory in your computer. This is done by paging, that is, taking some chunks (called pages) of memory not being used right now, and storing them on disk until they are needed again. (This is also called "swapping", even if that term originally meant writing all the memory of a process to disk, not just parts of it.)

And to complicate it even further, some modern operating systems such as Linux and MacOS X (but, I am told, not Windows) overcommit when they allocate memory. This means that they allocate more memory addresses than can be stored on the computer, even using the disk. For example, my computer here with 32 gigabytes of physical memory, and just 4 gigabytes available for paging out data to disk, can't possibly allow for more than 36 gigabyes of actual, usable, virtual memory. But malloc happily allocates more than one hundred thousand gigabytes. It is not until I actually try to store things in all that memory that it is connected to physical memory or disk. But it was part of my virtual memory space, so I would call that too mapped memory, even though it wasn't mapped to anything.