A tricentennial is a 300-year anniversary. If something has been around for a whole 300 years, it's probably worth talking about.
The prefix tri- means "three," and the root cent means "hundred." Add the suffix -ennial, derived from the Latin annus, meaning "year," and you get tricentennial: literally, "three hundred years." You'll usually see this word when people are discussing the anniversary of the founding of countries or other important institutions. Don't confuse it with triennial, a "three-year anniversary." A tricentennial celebration is definitely going to be a bigger deal than a triennial one.