Depends on the source of light but A) the sensation is an automatic response to protect the eyes and B) because light does burn.
As important as our eyes are, they’re an extremely sensitive set of organs. Because of that, our bodies have evolved a bunch of mechanism to automatically try to protect them from drying out, or contaminants or impacts (blinking and eye fluids). And that’s just the outside, we also have light sensitive receptors that connect to the optic nerve that can potentially be damaged if exposed to extreme sources of light for long enough periods of time. So the sensations of our eyes burning is just a series of steps our body and brain try to make us blink and maybe turn away to protect our sensitive eyes.
Also, a bright source of light is actually just burning our eyes too. Light is still energy and when it collides with tissue, it imparts some of that energy into the tissue it collides with. That’s going to potentially cause burns and, once again, our eyes are just not that durable.
Light carries energy. When it hits something, that energy gets transferred in part. Light is electromagnetic radiation after all.
Your cells can only take so much energy before they get damaged.
Our eyes evolved to be sensitive enough to work in normal lighting conditions on earth. That sensitivity goes both way, there’s only so much light our eyes can take. It was better for our eyes to be more sensitive than be able to take looking directly at the sun for example.
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