The Oxford Learner's Dictionary defines diversity as "a range of many people or things that are very different from each other." Based on that definition, there could be limitless different types of diversity. I will give you a few examples of types of diversity which are commonly referred to in the world today.
Religious diversity refers to people of different religious backgrounds. So, if an open-plan office were to be shared by a Muslim, a Christian, an atheist and two Buddhists, this office would be an example of religious diversity in the workplace.
Age diversity, quite obviously, refers to peoples ages, and breaks society down into various groups such as Baby Boomers, which is a term talking about people born between 1945 and 1964. After the Baby Boomers came Generation X, who were born between 1964 and 1979. With that in mind, many family reunions become great examples of age diversity in practice.
It's hard these days to find a society in which cultural diversity has not become prevalent. Cultural diversity refers to people of different cultural backgrounds. These groups live and work in close proximity all around the world, creating culturally diverse societies.