The phrase "to stop up" means to block or obstruct something, usually referring to a passageway. It can be used in various contexts such as plugging a hole with cement to prevent water from flowing out, blocking an air vent to keep cold air inside during winter, or sealing a door to prevent someone from entering. The phrase is often used in the past tense when referring to something that was done previously, for example "I stopped up the drain last night".