When an exoplanet orbits a star, the star pulls the exoplanet by gravity.
But Newton's third law says that if the star pulls the exoplanet, then the exoplanet must pull on the star by an equal but opposite amount.
The gravitational pull on the star by the exoplanet causes the star to move in space. The star moves in a small circle.
We can measure very accurately the speed that a star is moving in space by the doppler effect. When a star moves towards us, its light becomes slightly bluer, when it moves away it becomes redder. We can measure these changes very accurately and so we can tell when a star is moving in a small circle.
If we see a star moving in a small circle, we know that there must be an exoplanet orbiting the star. This means that we can "discover" an exoplanet even though we can't see it directly.