How do textures work?

I’m a beginner in game design and textures have been bothering me. How do they work in video games? Here’s what I mean.

Can textures change between resolutions in settings?

Or is it tied to screen resolution? As in your game has 4k textures but the user sets the display to 1080P. And if this is true then what resolution should the textures you put in the game be?