Hydrogen water or hydrogen-rich water (also called hydrogen-enriched water) simply means normal water (H2O) that contains dissolved hydrogen gas (H2) For example; there are carbonated waters or beverages (soda pop), which contain dissolved carbon dioxide gas (CO2), or oxygen water, which contains dissolved oxygen gas (O2). Similarly, you can have water that contains dissolved hydrogen gas.
Think of it this way: you can make hydrogen water by taking a tank of hydrogen gas (just like tanks of helium used to fill balloons or tanks of oxygen gas used in hospitals), and bubbling it into a glass of water. There are also many other methods to make hydrogen water, but this may help you better understand what hydrogen water is. It is simply water that contains dissolved hydrogen gas.