Using 4K Skyrim Textures when running 1920 x 1080 display resolution?

A 4K texture, does not require a 4K monitor.

In short, the graphics pipeline for getting "pretty pictures" on a screen is, with some hand-waving to simplify things:

• You have a 3D model, that looks like a thing - e.g. "a tree"

• You have a texture, which is just a 2D image of colors

• The texture is mapped to the model, such that each point on the surface of the 3D model (split into triangles), has a co-ordinate on the texture. i.e. points to a specific pixel on the texture. It's like mathematically wrapping a candy-bar wrapper around the chocolate inside.

• When you view this in game, Maths™ is used, which maps each point on the 3D model, to a pixel on your screen.

• As each point on the 3D model, is already mapped to a pixel in the texture. You can now set the color of that pixel on your monitor - to the color from the texture.

Note, the obvious things now:

• There are infinite points on a 3D model (look at your hand, find two points - you can keep finding a "half-way" point mathematically, infinite times)

• There are a limited number of pixels in the texture map. It has a width and height, and there is clearly no such thing as half-way between two pixels - it's either pixel 1, or pixel 2.

Therefore, to map each point on the model to a pixel in the texture, means some points will share a pixel. In game, when you zoom too far in - this means you either get pixelated looking images, or if they use any kind of filtering (*all modern games do), you'll get a nice big blurry spot.

A 4K texture just has more pixels to sample from. So more points on the model will have their own unique pixel. That is, you could get much closer to it - and you will still see details.

The resolution of your monitor only matters after this point. The model will still be rendered using the high-quality textures, even if your monitor is so bad - that you'd have to stand right next to the model to see any difference.

I can't comment as I do not have the necessary reputation, but I wanted to add on to Bilkokuya's excellent answer.

Two of the main important factors regarding whether you can see a difference with higher-resolution textures is both your distance from the object (which Mixxiphoid pointed out), as well as the size of the object. IOW, how much area that texture needs to be stretched over.

1K textures might look fine on an apple right in front of your face, but 1K textures on a mountain in Skyrim at the same distance might look very poor.

In general, I would consider high-resolution textures for anything large or frequently seen close-up.