There are a variety of metrics commonly used to measure storm size. The most common metrics include the radius of maximum wind, the radius of 34-knot wind (i.e. gale force), the radius of outermost closed isobar (ROCI), and the radius of vanishing wind.
Size plays an important role in modulating damage caused by a storm. All else equal, a larger storm will impact a larger area for a longer period of time. Additionally, a larger near-surface wind field can generate higher storm surge due to the combination of longer wind fetch, longer duration, and enhanced wave setup.