As eliminate means "get rid of or do away with," it has become used to refer to the end of a problem or even an entire species. We need to eliminate sources of pollution in order to maintain a healthy world.
The original literal meaning of eliminate was "to thrust over the threshold and out of doors, to kick out," but the 18th century saw the word expand to mean "to exclude," and later to ridding the body of waste. The verb then came to refer to getting rid of anything, such as a problem or foul odor. The word took an ominous turn in the 20th century, when we saw man-made pollution eliminate whole species, and war, hate, and famine nearly eliminate whole groups of people.