Something that's unconquered hasn't been taken over by a military, beaten in a competition, or accomplished. A lifelong mountain climber might mention that Mount Everest is the last unconquered climb on her list.
During World War II, Germany invaded and conquered many European countries, but a few, including Sweden, remained unconquered. To conquer is to completely control by force, especially military force. You can also conquer something figuratively, like when you conquer your anxiety. If you're still afraid of flying after years of struggle, that's an unconquered fear.
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