Your eye can adapt to a huge range of brightness levels. This is how you can see both under moonlight and in daylight even though the latter is literally thousands and thousands of times brighter than the former.
One of the ways it does that is by contracting your pupil to a smaller hole to let less light in. A side effect of that is this focuses the incoming image with greater sharpness. In particular, the [circle of confusion](https://en.wikipedia.org/wiki/Circle_of_confusion) gets smaller and the [depth of field](https://en.wikipedia.org/wiki/Depth_of_field) gets larger. The latter means that most of what you are looking at is simultaneously in focus, which is, I think, a big part of that “OMG I can see in HD” effect.
What we perceive as sharpness is largely influenced by local contrast – large differences between light and dark tones in the same small areas of the scene. When direct sunlight falls on a scene, the lights are lighter, making a greater contrast with the local darks. We perceive this increase in local contrast as increased crispness/sharpness.
Edit: clarity.
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