To conquer is to defeat someone or something, usually with force, like army troops that conquer enemy territory, or your lunchtime hunger which you conquer with a sandwich and cup of soup.
To correctly pronounce conquer, accent the first syllable: "CON-kur." It comes from the Old French word conquerre, meaning "defeat, vanquish." Use conquer to show you've gained control over something, like doing breathing exercises as the airplane takes off to help you conquer your fear of flying. You'll hear people say they've conquered Mount McKinley, or the Appalachian Trail. It means they've hiked and climbed the whole route, not declared the place theirs alone.