This allowed the OS to compact the memory heap, move all the relocatable blocks in one corner and allow further contiguous blocks to be allocated.
Of course, this is a primitive concept these days, but it allowed amazing pieces of software to exist on very, very small memory systems.
(This kindles some fond memories of MacOS classic development along with the Inside Macintosh books...)
IIRC the 68030 was the first 68k CPU that had one built-in.
Not that it mattered for AmigaOS. Commodore always used the cheaper versions without MMU.
Here's some surprisingly thorough documentation on this:
http://wiki.amigaos.net/wiki/Exec_Memory_Allocation
However, the MMU is not used for memory protection, not even on Amiga OS 4.
Edit: OK, so not entirely true... See this for more: http://www.os4coding.net/forum/memory-protection-support
I think there was similar issues with (classic) Mac OS and Windows 9x.