NASA went through some pretty complicated steps to find the evidence for water. The bare bones essence of what they did is this: they fired a radio wave at the poles of Mercury and measured what bounced back. The results were astonishing. There found pockets of highly reflective "stuff" at the bottom of what appeared to be craters on either pole. This significant because water ice is highly reflective in the radio wave spectrum. Not only that, but radio waves bounced off of water ice tend to be depolarized, and that's what happened to these radio waves. They came back depolarized.
Mariner 10, the last spacecraft to visit Mercury. Source
If Mercury is so hot, then how is it possible that there can be water ice? The answer to this is actually pretty clever. Mercury has a 3:2 orbital resonance around the sun, which, in English, means that it has a day of 176 Earth days. Every part of Mercury gets blasted by the sun eventually, so it stands to reason that any water on its surface would evaporate away into space (given Mercury's low mass). And while it's true that any water on Mercury should get blasted away it is also true that Mercury has a lot of impact craters. The poles of Mercury never get close to facing the sun, so there are regions in some of the deeper craters on the poles where light never shines. And because Mercury doesn't have an atmosphere, there is no hot air to heat the insides of these craters. It is therefore possible to have water on Mercury.
Locations of water on Mercury. Source
NASA's official claims don't exceed much more than what I have already said, but unofficially, there are some fascinating things related to their findings. It has been estimated that there might be as much as 1 trillion tons of water ice on Mercury. That is a lot of water. But what's even more fascinating is that there is evidence of water existing on slightly warmer parts of Mercury, surviving due to an insulative layer of... something. This "something" that keeps this water from melting could very well be organic matter. I'm not just talking about stray carbon atoms. It has been speculated that this insulating layer is composed of complex organic molecules indicative of either early life or the beginnings of life.
Life on Mercury? Could it be true? I don't know the answer to these questions, but it would be amazing to think that there could be something alive, or something that was once alive, on the hellish surface of this barren planet.