I couldn't get a clear answer from
the website which was promoting hydrogen (generally in solution with water, after running it through an electrolysis machine) as to what exactly hydrogen
does.
H2, like other gaseous-signalling molecules (e.g. NO*, CO, H2 S), modulates signal transduction, protein phosphorylation, and gene expression, which provides its anti-inflammatory, anti-allergy, and anti-apoptotic protective effects.
They seem to go back and forth on whether hydrogen is an antioxidant or not. I'm no Doctor Science over here but I don't know if an extremely flammable gas is really the best way to prevent oxidation reactions.
Also the same website sells water bottles with little electrolysis machines in the bottom...which apparently you can plug a tube into and breathe from?? But I couldn't find anything in the product description about it so idk if you're breathing pure oxygen, pure hydrogen, or both, or what.

Oh and in case your water is too heavy (as in, literally, it has too much mass), they also sell deuterium-depleted water, with a lower concentration of deuterium than in normal water. If you just want to lighten up your water a little bit, you can get an 18L pack of bottled deuterium water at 125ppm for £75, but if you REALLY want to drink less deuterium they go all the way up to 18L of 25ppm deuterium water for only £275.
As a comparison, the bottled water I can buy at Kroger costs approximately £3 for 18L, so if you want low-deuterium water you're paying at least twenty five times as much for water that has 17% less deuterium.