Total Solar Eclipse in 1999; Credit & Copyright: Viatour Luc
Solar eclipses are dramatic events -- for a few minutes, the sun darkens, and a small area of the Earth is plunged into night time. Eclipses have tested human powers of record-keeping, observation, and inference for millennia. The Babylonians observed Solar eclipses for centuries, and developed a scheme that was able to predict them with an accuracy of (days?).
With the realization that the Earth and other planets revolved around the Sun, Solar Eclipses became a key tool to study the distances to the inner planets. Observations of the transits of Venus and Mercury were used to help determine the distance between the Earth and the Sun (although my understanding is that another technique proved more accurate), which in turn is the first step in the "distance ladder" by which astronomers determine the distances to stars.
The eclipse of 1919 proved to be important in verifying a prediction of Einstein's theory of gravity, General Relativity. Einstein had put forward a prediction of how far a star's apparent position would move as it's light was bent when it neared the limb of the eclipsed sun. That prediction was verified in a famous scientific expedition to watch the eclipse.