If to design (https://lib.hol.ink/index.php?topic=7.0) is to make intentional decisions, the principles of design represent the logic designers consider and reflect on when making those decisions. We use them to describe the relationships between two or more elements (https://lib.hol.ink/index.php?topic=13.0) present in a work of art, with each element representing a decision made by the artist as they created their work.
The principles include things like contrast, unity, balance, gesture, rhythm, and movement.
For example, if we place a shape element with a high (light) value and another shape element with a low (dark) value, we've decided to use contrast.
If we then add lots of similarly light shapes around it and never any other dark ones, the low value both contrasts the rest of the image and is unbalanced, so that dark spot attracts the viewer's eye. Whereas the high values are balanced and thus do not attract the eye.
Each principle is relevant for a variety of reasons, and they affect one another.
Contrast affects where the focal points for the eye are (as discussed), but it also affects the overall mood of an image (high contrast tends to feel a bit more aggressive) and how easily its subject is identified (the brain needs to see a recognizable high-contrast shape to identify something at a glance).
And when something contrasts, that often implies a lack of unity, although not always.
For example, let's imagine we're making an arrangement of primitive shapes that go up from a 3-sided triangle to a 10-sided decagon. That decagon contrasts every other shape, just as the triangle contrasts every other shape. But choosing to add that decagon adds unity to the composition, because it supports the pattern, whereas choosing to add a duplicate of another shape would have reduced the unity despite also reducing the contrast.
These relationships can get very complicated and interconnected. And yet, like the elements themselves, the principles tend to be overlooked by developing artists because of how early they are taught and how simple their individual components seem. The reality is that developing an intuitive understanding of these ideas -- and fully grasping where and why they're used -- is difficult and takes time.