I’m not the best person to explain this, but I think you are referring to the “depth of field” of the images.

This is either artistic choice or limitations of the lens used. I think these images use a combo of both of those things.

Owl photos are usually taken from far away, so the distance to the subject is very far, and the focal length of the large lenses sets physical limits for the lens to have everything in focus.

Some long lenses have fixed apertures, the hole that lets light through the lens into the camera’s sensor. Others are adjustable, but the photographer may still want that blurry background there to draw your focus to what is in focus more, in this case they wanted to highlight not just the owl, but also the tree. By having most everything else blurred, it may not appear as natural, from how our eyes work compared to a camera and lens, but now instead of spending time looking at the background, you still get the general “feel” of the background while all your attention is placed on what the photographer wants you to be looking at.

This short video (about 3 min, I copied the annoying into) goes into the 3 elements I mentioned and shows you the resulting blue or non-blur.

There are also image editing tools that can enhance this. On my Pixel, Google calls it portrait blur.