The Moon is a particularly harsh mistress (with apologies to Robert Heinlein). Not only is it airless, but it also has no shielding from radiation (we do because of the Van Allen belts), meaning that the only way that you can build lunar habitats is to build them underground. The current thinking is that such habitats would likely consist of the equivalent of inflatable balloons within lunar lava tubes, eventually supplemented by additional boring. Existing tubes obviously reduces the complexity of establishing a base dramatically.
So why put a base on the moon? The biggest is that the moon has only 1/6th the gravity of Earth, meaning that you need much less energy to escape its gravity well. Additionally, no atmosphere means no air resistance, meaning much less ablative shielding necessary on spacecraft (you may even be able to get away with ion impulse engines at that point). Anchoring a satellite in orbit around the moon makes it much easier to develop deep space telescopes in orbits that always keep them away from pointing at both the Sun and the Earth. Low-gravity manufacturing becomes feasible. The moon also becomes an ideal location for microwave collection systems, which can then be beamed to satellite transmitters and from there to Earthside waystations.
Of course, it also becomes a political football, a point brought up extensively since the 1950s.
The Moon was formed in part by the ejecta from Theia's collision with Gaia (the proto-Earth) about 3.8 billion years ago, and in part by the partial disintegration of Theia as it approached Earth's Roche limit. As a consequence, it is relatively differentiated, and has more oxygen, titanium, aluminum and iron in its crust than the Earth does (although almost no helium, hydrogen, as measured by concentration. Consequently, mining would serve two purposes - extracting minerals, and enlarging habitats.
This is one reason that I don't understand the rush to Mars. Mars only becomes feasible once the Moon is colonized, and we are a long way from even that just yet.
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