Built in the 1840s with the expectation it would the city hall of the capital of the country. It's a common myth that it was the site of Canada's parliament during the time when Kingston was capital, but it was always intended to be, and used as, City Hall.
Stylized depictions of City Hall and the clock tower are standard symbols of the city, pretty ubiquitous. Like in the municipal logo:
And even the symbol used to indicate municipal parking: