To wriggle is to squirm and twist quickly. Think of how hard it is to hold a rambunctious puppy as it wriggles in your arms.
Wriggle sounds a lot like wiggle, and the two words very nearly mean the same thing. There is a subtle difference, though: when you wriggle, you twist, turn, or bend as you move. When you wiggle, you make more of a back-and-forth motion. In fact, these two near-homonyms have completely different etymological sources. While wiggle stems from a Germanic root meaning "cradle," wriggle's root means "to turn or bend."