While prevaricate basically means to lie, it also has the sense of making it hard to know exactly what the lie was. You talk in a confusing way, go back and forth, and as deliberately as possible mislead someone. Government officials, bureaucrats, and sneaky types prevaricate in the hopes that it will be too difficult to figure out whether they've been doing something wrong. Don't prevaricate with your parents — it will definitely make you look guilty, but they just won't be sure of what!