A starshade is simple in concept: put something between the telescope and the star. The difficulty is everything after that sentence.

Blocking without blurring

The shade must suppress starlight while allowing light from a faint nearby planet to reach the telescope. Its petal edges are shaped to control diffraction.

Flying a shadow

Because the shade and telescope would be separated by large distances, navigation becomes part of the optical system. The spacecraft must know whether the shadow is centered.

A slow instrument

Moving between targets would take time and fuel. Mission planners weigh every observation against the cost of repositioning the shade.