Presumably it's somehow related to memory? What would
sudo cat /dev/urandom > /dev/mem
do? Trash all RAM? All non-kernel virtual memory? None of the above?
It provides access to the system's physical memory.
Yes -- it could cause all sorts of problems. A reboot should fix you, but bad things can happen very easily. Be careful! :-)
/dev/mem provides access to system physical memory, not virtual. The kernels virtual address space can be accessed using /dev/kmem.
It's primarily used to access IO memory addresses related to peripheral hardware, like video adaptors.