Prevarication is when someone tells a lie, especially in a sneaky way. A child might use prevarication to avoid telling the whole truth about how the kitchen window got broken.
While the noun prevarication is mostly just a fancy way to say "lie," it can also mean skirting around the truth, being vague about the truth, or even delaying giving someone an answer, especially to avoid telling them the whole truth. In the 16th century, the word was used to mean "going astray," or "stepping out of line." It comes from the Latin root word praevaricari, which literally translates as "walk crookedly."