Literally: the people.
If you were to take a survey of the world’s languages, you’d find that not a small majority of them have a word for ‘the people,’ and that word would most likely also function as the common name for the people of that culture. Which is just a way of saying that Diné is what you call a Navajo in the Navajo language.
You can also say Dine’é to refer to the Navajo Nation, or to the Navajo people as a tribe or group rather than as an individual. Apart from using Diné as a word for Navajo, there is a more general diné that can be used to describe other groups of people.
For example, Naakai dine’é is a clan (dóone’é) that refers to the Mexican People, which denotes an ancestor of that heritage.
You will also see the word dineh written instead to avoid pronouncing it as “dine.”