Why would astronomers want to eclipse the Sun? I've heard that some astronomers are building an artifical solar-eclipse ship, that should help us to dim the diffraction of the Sun.

Why don't we just wait till night? What is the function of the eclipse-ship really?
As Conrad Turner notes, that talk is about a device for blocking the light from another star (one you think might have planets orbiting around it). It's not for blocking the light of the Sun!

If you try to look at a planet orbiting around another star, the glare from the star makes it very hard to see the planet. By placing a specially shaped device in front of the telescope (in this case, thousands of kilometers in front), between the telescope and the star you're interested in, you block most of the light from the star, but not the light from any planets near that star.

https://en.wikipedia.org/wiki/New_Worlds_Mission