Sciurus is the Latin word for squirrel, and sciurid means squirrel-like. The sciurids are the family of rodents to which all squirrels (and marmots/woodchucks) belong.
The name itself describes the hallmark of all these rodents: their big bushy tail. As explained by this New York DEC brochure,
sciurus is derived from the Greek skia (shadow) and oura (tail). Anyone who’s seen a squirrel run across a street or lawn with its tail undulating and waving can appreciate the concept of shadow tail. And typically, a squirrel sits with its tail curled over its back– "in the shadow."
One member of the sciurids is the always-amazing (and rarely seen) flying squirrel. You can find some great videos of these creatures at FlyingSquirrels.com.