Specifically, it's a common noun (not a proper noun like "London" or "John") and a concrete noun (it refers to something that can be experienced with the senses).
However, it's important to note that "farewell" can also function as an interjection (an exclamation expressing emotion, like "Wow!" or "Ouch!") and as a verb (meaning "to say goodbye").
The grammatical function of "farewell" depends on its context in a sentence.