So I saw this and was surprised that my location history was turned on. Pretty creepy. I turned it off, but I can still view all my movements for the period when it was turned on, and there doesn't seem to be any way to tell them to erase the data. Do Google make any guarantee that they don't store your location data when you have this "feature" turned off, or could it be that they still store it and just don't show it to you? In any case I am sure there is no way of turning off the ability of the police and intelligence agencies to find or track you through your phone. It is crazy that we walk around with these little spies in our pockets.
The 'Delete All History' link that appears underneath the calendar will delete all your location history. The settings cogwheel in the top right will allow you to turn off location history.