A centenary is the hundredth anniversary of some event. When your great grandfather turns 100, his birthday party will be the centenary of his birth.
If your town is celebrating its centenary, that means it's exactly 100 years old. You can also use this word as an adjective, to describe something that's been around for a hundred years: "The orchestra's centenary concert will happen next summer." Centenary comes from the Latin centum, "hundred," which is also the root of its synonym, centennial.