Many animals can see into the ultraviolet part of the spectrum, though the ability is most prominently seen in birds and insects. Still, there's evidence that at least some reptiles can.
Accordingly, I'd guess that the biofluorescent patterns help the turtles stand out against their backgrounds, and so help the turtles to find and recognize each other.
Kind of like how many flowers have "nectar guides" that are visible in ultraviolet, and help guide birds and insects to the good stuff.
A Cinquefoil flower in visible light on the left, and how it might look to an animal that can see ultraviolet light on the right. The nectar guides are invisible in "normal" light, but clearly visible in ultraviolet.
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“The greatest way to live with honor in this world is to be what we pretend to be.”
As an aside, though it's not entirely clear why, scorpions are biofluorescent. The standard way to hunt scorpions in the desert is to go out at night with a black light and shine it on the ground. Any scorpions that happen to be nearby will glow a vivid blue-green.
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“The greatest way to live with honor in this world is to be what we pretend to be.”
Great. Now I have to balance knowing that I have the power to know if scorpions are around versus seeing a thousand glowing eyes staring back at me in the desert.
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"Her eyes in certain light were violet, and all her teeth were even. That's a rare, fair feature: even teeth. She smiled to excess, but she chewed with real distinction." - Eleanor of Aquitaine