google history
 

Forget what it's called but when you are trying to type something on the address bar or search, on google
and you type in 1 letter and google trys to guess what you are trying to type, like a history of previous searches.

how do you remove that history (not sites) but searches

so when someone else sits at the computer to search google
they don't see all the stuff I searched for recently

Turn off AutoComplete. It's dependent upon your browser.

You have to select the entry and press delete keyboard button.

try switching to another browser and you wont see it