Water, H2O, is an ubiquitous molecule in the universe and very common in our Solar System. There is water in the atmosphere of Venus, drenching the Earth, as permafrost and polar caps on Mars, and it is the major component of several moons of the outer Solar System, as well as much of the debris farther out in the Kuiper Belt and Oort Cloud. So it came as quite a surprise in the 1960s, when samples were brought back from the Moon for the first time, that the Moon was anhydrous, or without water. This was more profound than the lack of groundwater or permafrost; the water that is incorporated in many minerals on Earth was completely absent from lunar minerals.
This, actually, was predicted by the early lunar scientists. Water will evaporate at any atmospheric pressure and ice will sublimate at lunar temperatures and vacuum. Given the energetic solar radiation and wind the water molecules would be atomized and accelerated out of the weak lunar gravity field. Otherwise there would be a slight atmosphere of water and other volatives around the moon.
Though some scientist theorized that ice might be found in the cold polar craters that have not been exposed to solar radiation for billions of years, especially if the ice was covered by lunar regolith, it was not until 1994 that evidence of lunar ice was found by the Clementine lunar probe. Ice has a left-polarized radar refelection that was observed by Clementine at both lunar poles. The evidence for ice on the moon was greatly strengthened by Lunar Prospector's neutron radiation data. Lunar Prospector observed the background or cosmic neutron radiation and the neutron radiation from the moon as it orbited. It found back scattered neutron energy consistent with hydrogen but only at the poles. Water was further confirmed by NASA's LCROSS lunar impact mission and India’s Chandrayaan-I lunar orbiter radar. The estimate of lunar ice has risen to millions of tons, somewhat more on the north pole than south.
Water and Life
Water is of course a primary component of life as we know it. The near total lack of water on the Moon struck quite a blow to lunar settlement plans. One of the components of water, oxygen, is abundant on the Moon, since many lunar rocks are oxides. It will take energy and machines to win this oxygen. Some hydrogen is also trapped in the lunar regolith, deposited by the solar wind, but it is very thin (Blacic, ref. below, states 100 ppm by weight) (ppm = parts per million). Finding hydrogen deposits in the cold trap areas of the lunar poles, presumably water ice but possibly some other ices as well, such as methane (CH4), has caused many planners to regard the poles as initial base candidates. Such hydrogen as can be found there, in whatever form, should probably not be squandered, but kept religiously in the lunar economy, being circulated and recirculated as water, carbohydrates, etc.
Water and Fuel
Some people see the ice deposits at the lunar pole cold traps as a source of cheap rocket fuel. Hydrogen, though, is used to reduce metal oxides to metals releasing the oxygen in the ore as water. The water would then be hydrolyzed to recycle the hydrogen and produce pure oxygen. Use as a fuel would be extremely wasteful of a vital ore processing resource, at least until a better or cheaper hydrogen source can be found from comets or outer moons. Other substances, such as aluminum or magnesium with oxygen should be used for rocket fuel. These elements are very abundant on the moon.
Water and Glass
In Lunar Bases and Space Activities of the Twenty-first Century (W.W. Mendell, ed., 1985), James D. Blacic of Los Alamos National Laboratory wrote about "Mechanical Properties of Lunar Materials Under Anhydrous, Hard Vacuum Conditions: Applications of Lunar Glass Structural Components" (p.487). He states that, "Hydrolysis of Si-O bonds at crack tips or dislocations reduces the strength of silicates by about an order of magnitude in Earth environments." This means that lunar anhydrous glass is about an order of magnitude (10x) stronger than Earth glass we are familiar with, and can be useful as a structural component. Experiments confirm this. Anhydrous lunar glass or glass composites can be made into "a lightweight structural material with several hundred thousand psi tensile strength."
This also has implications for geology and material handling on the Moon. The glass fraction of regolith will be much harder than we would otherwise expect, and this will make tools and machines wear more quickly. In geology, it implies that the glass matrix component of lunar basalts (about 52% ) is much stronger on the Moon than on Earth, and this may translate to a much wider span being supportable than the roughly 340m theoretical maximum based on simple extrapolation of Earth basalt to the Moon (an order of magnitude, Earth maximum being approximately 30 meters). This possibility is supported by circumstantial evidence (Coombs & Hawke, 1992) that lunar lavatube caves may reach a kilometer or more in span (diameter). Note that due to the evidence of flowing water on Mars, its basalt may be no stronger than Earth basalt, and maximum size of its lavatubes may be roughly 150 meters (back of envelope calculation).