This is because "Cherokee" refers to a specific Native American tribe and their language. Capitalizing it demonstrates respect for their cultural identity.
Examples:
* Correct: The Cherokee language is fascinating.
* Correct: She is a member of the Cherokee Nation.
* Incorrect: He is learning the cherokee language.
Remember, proper nouns (names of specific people, places, and things) are always capitalized. "Cherokee" is a proper noun, even when used as an adjective.