You're describing a binary star system. In a binary star system, two stars are gravitationally bound to each other and orbit around a common center of mass. This is very similar to how the Moon orbits the Earth.

Here are some examples of famous binary star systems:

* Sirius A and Sirius B: The brightest star in the night sky, Sirius, is actually a binary system. Sirius A is a large, bright star, while Sirius B is a white dwarf.

* Alpha Centauri A and Alpha Centauri B: The closest star system to our own Sun is a binary system consisting of two sun-like stars.

* Cygnus X-1: A black hole paired with a massive blue supergiant star. This is a very powerful and fascinating system.

There are many, many other binary star systems in the Milky Way galaxy. In fact, they are thought to be more common than single stars!