When you're designing C programs for embedded systems, or special purpose programs that need to refer to the same memory (multi-processor applications sharing memory) then you need constant pointers.
For instance, I have a 32 bit MIPs processor that has a little LCD attached to it. I have to write my LCD data to a specific port in memory, which then gets sent to the LCD controller.
I could #define that number, but then I also have to cast it as a pointer, and the C compiler doesn't have as many options when I do that.
Further, I might need it to be volatile, which can also be cast, but it's easier and clearer to use the syntax provided - a const pointer to a volatile memory location.
For PC programs, an example would be: If you design DOS VGA games (there are tutorials online which are fun to go through to learn basic low level graphics) then you need to write to the VGA memory, which might be referenced as an offset from a const pointer.