Such a base would be useful for learning to live and manufacture in space, for space based research, for launching missions to Mars (and elsewhere), and for building a large radio telescope (protected from radio interference experienced on Earth). Oh, and there is an opportunity for tourism too.
Such a base would represent our first giant leap off the planet and boost space innovation.
In addition, the moon contains Helium3 which would be useful in producing a new generation of fusion reactors for either generating electrical power [although there is plenty of opportunity for harvesting vast amounts of solar energy], or for rocket propulsion to other planets, and beyond.
See more details in the article.