In a unilateral mistake, both parties have agreed to a standard term, but one party believes that term refers to something else. It's very common, unfortunately.
THe best example, the one you find in textbooks, is the "screw" example. If a contract specifies the use of screws to build a deck, Party A may think of one type of screw and Party B may think of a different type of screw. If Party A is correct, but both parties don't think to specify, it's a unilateral mistake :)