I can run a command like this:
tim@Hairy:~$ echo Hello
Hello
Then I can run the command !! and it does it again:
tim@Hairy:~$ !!
echo Hello
Hello
I can even run it with another argument to the previous command:
tim@Hairy:~$ !! World
echo Hello World
Hello World
So what is the !! actually doing? I have struggled to search for it because a Google for !! is fairly... pointless.