Chemistry - What is hydrogen-rich water?
Solution 1:
Hydrogen water is a solution of molecular hydrogen $\ce{H2}$ in water, which shouldn't be confused with acidic or basic solutions. The first scientific reference to hydrogen water appears to be in the journal, Nature Medicine which can be accessed here if you have a personal or institutional subscription to the journal. The claim is that molecular hydrogen can serve as a mild reducing agent and therefore has antioxidant properties; namely, it can reduce hydroxyl radicals: $$\ce{H2 +2 OH\cdot -> 2H2O}$$ The article has generated a considerable amount of research, with well over 300 journal articles citing this work originally published in 2007. There seems to be some merit to the claim although in my brief scan of the abstracts, there does not appear to be a large body of evidence suggesting that commercial products are beneficial. One such article, which is publicly accessible is here. As mentioned in another answer, the commercial product approach to generating hydrogen water appears to be the oxidation of magnesium in water, which generates $\ce{Mg^2+}$ ions. As with any other nutritional supplement, I would be very wary of entering this type of treatment without consulting a professional. Magnesium is an important nutrient, however at high doses it does show signs of toxicity.
Solution 2:
I was completely unaware of the concept of hydrogen-rich water, and although there is a lot of misinformation and quackery around it, a quick search on Google afforded an article (whose quality I cannot vouch for). It would seem that hydrogen-rich water is nothing but regular water with dissolved hydrogen gas. You could simply pump $\ce{H_{2(g)}}$ into some water, but there is a smarter way to do it, by producing the hydrogen in situ via the addition of reactive metals such as magnesium, according to the following reaction:
$$\ce{Mg_{(s)} + 2H2O_{(l)} → Mg(OH)2_{(aq)} + H2_{(g)}}$$
Producing the hydrogen directly inside the water also seems to temporarily supersaturate the solution and increase the amount of hydrogen dissolved, because the equilibrium solubility of hydrogen gas in water is tiny, only around 16 mg per kg of water at 20°C. The exact mechanism by which hydrogen-rich water has medicinal properties I do not know, and that would probably be best answered on Biology.SE if you're curious. It is conceivable that the dissolved hydrogen gas could act as an antioxidant, though relying on the distribution of a gas across the body seems a bit strange (there are gaseous substances known to be important for our metabolism, such as $\ce{NO}$). I wouldn't rule out the possibility of it being nonsense before reading into it a lot more, though.