The idea of diversity in US society is generally used with reference to ethnic and racial diversity. When we say that there is diversity in US society, we mean that America has all sorts of different ethnic and racial groups living together within one society.
When we talk about diversity, we tend also to be talking about inclusion. We are talking about the idea that all of the diverse parts of US society are equally included in American society. This is in contrast to a system in which different ethnic groups were present in a society but in which many such groups were marginalized.
So, diversity in US society refers to the idea that America is a "melting pot" of many ethnic and racial groups, living together as equals.