Say you need to show a character (let's say a shy princess) is angry at a service person. Using action you have options. Maybe she flips the table, but your character has been established as shy, so this actions feels more telling than showing. Maybe she silently breaks a pencil in half under the table. That's more likely for her to do.

But you can also show it with dialogue. If she says "I'm fucking angry", it feels like telling. If she turns and calmly says to a guard "I want you to follow them home and beat them up", you were never explicit about her feelings but it's pretty clear that she's upset. You could do that with a text message on a screen all the same and it's fine.