Putting bases on the Moon means we can do more studies, experiments, etc. outside of Earth, particularly tasks that are difficult to complete by current rovers. Human physiology in low gravity situations, lunar geology, possibility of water and life outside of Earth, that sort of stuff. I’ll also echo what others have said about how the Moon could become a launching base for future explorations, given its lower gravity and lack of an atmosphere.

There isn’t a conspiracy by lizard men to set up a Death Star, this is driven by the curiosity of humanity and our desire to explore the unknown. The “race” to have the first base between Americans and Chinese is, like during the Cold War between the former and the Soviets, a push to be the first, trying to show that they are ahead in terms of technology and science. In a nutshell, it’s driven by curiosity and, at least partly, national pride.