Overproof rum is any rum with more than about 80 proof. Unfortunately the term does not specify the flavor or origin of the rum desired. Overproof rum is usually used to raise the alcohol content in an otherwise low-alcohol drink.
Most overproof rums are 151 proof, which make them great extraction mediums for homemade liqueurs. Gosling's, Wray and Nephew, Bacardi, Coruba, and Lemon Hart all make overproof rums.