It competes with iodine in the body. Iodine is one of those really important things that every cell in your body uses, and it's required for energy. This impacts many things, including, as the other anon pointed out, IQ. As an adult, it's more likely to show up as fatigue, mental and physical. It can even cause brain fog and things like that. Iodine is also important for your immune system, and many other things I'm sure I don't even know about.
Actually, iodine itself can be used as a sterilizing agent. I saw a study saying that you could replace the chlorine in a pool with iodine and it actually works better, aside from just being healthier. For that matter, when they fluoridate the water supply, not only does it compete with your iodine, but it competes with the iodine in your food as well, so it's a double whammy. Your food has less iodine to begin with, and you also have less, so you're getting hit twice. Maybe even 3 times, cause bromine, that they put in bread, also competes with iodine.
So, I'd recommend supplementing with it, to counteract what they're doing. You can stop reading here if you just wanted to know about fluoride and its relationship with iodine. For the rest, I'm going to explain how to make your own Lugol's iodine for super cheap.
Just dissolve 2 parts (in grams) potassium iodide with 1 part pure iodine (elemental iodine, iodine prills, iodine crystals, whatever they're calling it) in water, and you're in business. The recipe I used was 100g of potassium iodide and 50g of pure iodine in a liter of water. This makes an entire liter of a 5% Lugol's iodine solution, and only costs around $30. That's roughly 125g of iodine in total, or about 6.25mg per drop. This is a huge amount. If you take 50mg a day, as I've heard many recommending, this will last nearly 7 years.
Also, in my experience, it can take a bit for it to dissolve, but just keep stirring. People recommend to leave it overnight before using it. I'm not entirely sure why. Maybe it's just to make sure it's all dissolved, but I guess it can't hurt. Iodine is also reactive with metals, so don't leave it in contact with any metals. Store it in glass.
It will stain things very readily, and the fumes even seem to escape through, presumably, the rubber of the droppers that I have it in, and coats the surrounding walls. So, make sure to keep it well concealed if you're going to do this. I was taking 50mg at a time (rda is ~150mcg for reference. So, I was taking 333x that amount), and I noticed pretty much nothing happening, but it can be cumulative. Start low and see if you have any reaction, then up the dose as you care to. Not sure what would be a good maintenance dose. I've heard wildly different dosages recommended. I've heard most saying 50mg a day, but I've heard a dude saying he was taking 1 gram of it, and yet another recommending just 1mg. Different environments, foods, etc. will play a role in how much you should take.