Why were scientists so excited by transits of Venus?

Because it helped them make a very precise measurement of the distance between the Sun and Earth. This established the true physical scale of the entire solar system and the cosmos beyond.

In 1663, James Gregory, a Scots mathematician and astronomer, suggested that a more accurate measurement of the Solar Parallax could be gained from observations of the transit of Venus made from various widely separate geographical locations.

Halley realizes importance of transits in determining sun's distance during 1677. During a stay on the island of Saint-Helena, Sir Edmund Halley (1656-1742) observed a Mercury transit in that year and made careful note of the times of entry and exit of Mercury over the solar disk. He realized that if a transit would be observed from different latitudes on Earth, the different observers would see Mercury cross the Sun along at a different angle. This effect is known as parallax (this is even more noticable for Venus transits, since Venus is closer to us than Mercury, which increases the difference in angles) and could be used to determine an accurate Earth-Sun distance.

Halley published past and future transit predictions in 1691, then in 1716 he published a greatly refined version of a paper originally read before the Royal Society in 1691, entitled 'A new Method of determining the Parallax of the Sun, or his Distance from the Earth'. In the paper he championed the idea of scientists from various nations observing the 1761 and 1769 transits of Venus in as many parts of the world as possible. This, he argued, would result in a 'certain and adequate solution of the noblest, and otherwise most difficult problem' of accurately establishing the distance between the Earth and the Sun.

In 1716, Halley formally proposes Venus transit observations and shows how to use them to find exact value of the astronomical unit - the distance from the sun to earth. In his article published in the Philosophical Transactions and titled "A new Method of determining the Parallax of the Sun, or his Distance from the Earth" (http://www.dsellers.demon.co.uk/venus/ven_ch8.htm ) he notes:

"We therefore recommend again and again, to the curious investigators of the stars to whom, when our lives are over, these observations are entrusted, that they, mindful of our advice, apply themselves to the undertaking of these observations vigorously. And for them we desire and pray for all good luck, especially that they be not deprived of this coveted spectacle by the unfortunate obscuration of cloudy heavens, and that the immensities of the celestial spheres, compelled to more precise boundaries, may at last yield to their glory and eternal fame."