Science, exploration, and personal satisfaction. Don't underestimate that last; frontier exploration is a massive part of many of our cultures, but the painful truth is that there aren't any left on Earth. Everything's owned by somebody. Moving into space could have an almost religious impact down here.

The science is mostly geology and astronomy --- the moon is a great place for observatories --- but mainly it's engineering and life sciences; the moon makes a great place to learn about how to solve the kinds of problems that you have to solve when living somewhere like the moon. Which sounds tautological, but it's all stuff that we have no idea about and the moon, being on Earth's doorstep, as a good place to start.

Much further down the line, mineral exploitation. Trying to establish a proper presence in space by hauling everything out of Earth's gravity well is ludicrous, and the moon's the obvious place to go for resources. But that's much further down the line; we need to have people living on a regular basis on the moon first. Even learning how to do simple things like refining metal there is going to be hard. (See above, under 'engineering'.)