shut up

The phrase "callarse" (or more bluntly "¡cállate!") is the direct equivalent of telling someone to be quiet. The mental image is that of a physical lock being placed on the mouth, or a sudden cessation of sound, similar to hitting a mute button on a conversation. While "cállate" is the standard imperative, it can sound quite aggressive or rude depending on the tone of voice. In casual settings among friends, it is often used playfully, but in professional or formal environments, it is considered very impolite. If you want to be more polite, you would use "por favor, guarda silencio" or "podrías dejar de hablar, por favor."
In conversation
Friends joking around
¡No me digas que perdiste las llaves otra vez!
Don't tell me you lost the keys again!
¡Cállate! Es que me distraje.
Shut up! I just got distracted.
Used here in a playful, exasperated way between close friends.
Annoyed in a movie theater
¿Qué pasará ahora en la película?
What will happen now in the movie?
¡Cállate, por favor! No puedo escuchar nada.
Shut up, please! I can't hear anything.
Used to demand silence in a public space where talking is inappropriate.
Examples
Cállate un momento, por favor.
Shut up for a moment, please.
¡Cállate la boca, no quiero escuchar más mentiras!
Shut your mouth, I don't want to hear any more lies!
Me dijo que me callara, pero yo seguí hablando.
He told me to shut up, but I kept on talking.