To extirpate something means to destroy it completely, removing every trace so thoroughly that it can never come back. When scientists work to extirpate a disease like smallpox, they eliminate it from every corner of the world until it no longer exists anywhere. When gardeners try to extirpate an invasive weed from their garden, they dig out every root and seed, leaving nothing that could regrow.

Extirpate means removing something so completely and thoroughly that it's as if it never existed. You might read about efforts to extirpate an invasive species from an island ecosystem.

This is a strong, serious word typically used in formal writing about major efforts: scientific campaigns, environmental projects, or historical events. You wouldn't use it for everyday situations like cleaning your room or finishing your vegetables.