You seem to be mistaken in seeing only two universities in California. In fact, the two example you cite are University Systems, each with many universities under them. For example, the University of California system has UC Berkeley, UC San Diego, UC Los Angeles, and many more. The same is true for the other system.
In the end, one of the things to remember is that many of the US states are pretty big. California has a population of 38 million -- more than many countries in the world. It requires dozens of universities to educate its next generation, and for administrative purposes, these universities have been grouped into two systems (or, if you want to consider the community colleges as universities, into three). Other states have done the same.
These systems -- at least in most states in the United States -- do not usually provide any input into research or teaching. This is typically left to the individual university. Rather, the systems do things like property and land management, dealing with some financial matters such as issuing debt or bonds, providing political connections in the state legislatures, etc. In my current home state, the Texas A&M University System provides the administrative structure for the many universities under its umbrella, but the System itself is actually a rather small organization compared to the universities it oversees.