After completing one of the two main storylines, you can unlock the Movie Theater in Stardew Valley. The unlock method changes depending on which story you pursue, but the purpose of the Movie Theater stays the same. You can invite a villager to go with you to a movie to improve your relationship, assuming you invite them to a movie they enjoy.
How to unlock the Stardew Valley Movie Theater
The Movie Theater becomes available on the first day after a rainy or stormy night after completing all community center bundles or by purchasing all town upgrades via Joja Mart.
If you complete the community center bundles, the Joja Mart in town becomes abandoned, which opens up after a stormy night. Head inside and you can find the Missing Bundle.