Your iris (the coloured bit of your eye) is muscle. You focus on an object by using this muscle to squeeze or stretch the lens in your eye until the object you are looking at comes into focus.
If your eye is trying to focus on something very close to you the lens is being squeezed so that it gets more like a sphere than a disk. There is a limit to how far this can go, but you keep squeezing with your iris until it starts hurting.
It’s a bit like if you try to lift something really heavy, your arm and back muscles start to hurt.
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