The movement to leave Earth-That-Was stands out as a remarkable event in human history, one in which cross-cultural cooperation helped to achieve what some thought was impossible. In the effort to find a new home for humanity, the primary powers of the era - the United States of America and the People's Republic of China - worked together to create the necessary technology, manpower, and logistics for the largest migration of people ever known.
Overview
Once the exodus of mankind had begun, the close quarters and difficult survival conditions in space broke down traditional barriers of language and culture. After a full generation had lived and died in the massive convoy of ships slowly trudging from star to star, the average person was at least bi-lingual and had a very multicultural outlook. A person's ethnicity became far less important than competence and character.
Thus many generations later, the children of the Earth-That-Was don't think much back to the days of civilization, but continue the legacy by their almost universal fluency in both English and Chinese. Culture and language have both continued to evolve, with economics becoming a primary dividing line. It is easy to distinguish a person from the central planets from one born and raised out on the Rim. Slang and linguistic shortcuts are used on the frontier, though some have filtered back into the refined speech usually found on worlds of the Core.
English and Chinese
Folks in the 'Verse speak English or Chinese, one or the other being the dominant tongues most everywhere. It pays to know at least a little of both if you plan to get very far. Of the central planets, Londinium is primarily English-speaking, while Sihnon stands out as a center of Chinese influence.
Translation
Wash "speaking Chinese" to Zoë in episode 1 "Serenity."
Firefly does not translate what the characters are saying when speaking in Mandarin. If the viewer chooses to add subtitles on Netflix, the screen will display "Speaking Chinese" rather than translating what the character is actually saying. Nevertheless, each episode's individual wiki page contains a "Mandarin Translation" section.
Mutt Tongues
Hundreds of languages made the great leap from Earth-That-Was and most of them survive in pockets and ghettos on most worlds. Only rarely, however, will anyone encounter a community that speaks a non-dominant language exclusively. However, many of Earth's languages besides English and Chinese have spread across the 'Verse and are widely spoken by many people next to the two mentioned (and dominant) languages . Examples of such widely spoken languages outside of English and Chinese in the 'Verse include Russian, Hebrew, Arabic and Indian.
Cussin'
Human beings have happily fouled the gift of language with whatever inventive, vindictive, and insulting expressions they can imagine. While the traditional English swear words have survived intact, a few additional crude cuss words have been added to the common man's vocabulary.
The basics include Gorram ("Run! It's the gorram law!"), Ruttin' ("It's gettin' too ruttin' hot in here."), and Humped ("He's got a gun on us. We're humped!") Cursing in Chinese is considered more imaginative and expressive, and most everyone does it - at least when his mother has left the room.
The majority of Chinese language influence in Firefly is based on epithets and curses; however, some other terms, such as “mei-mei” (meaning “little sister”) are used between characters at different times, showing that there is more Chinese influence than is commonly used in the show itself. In addition, English-based epithets, generally adapted from current words, continue to evolve.
Fightin' Words
Some speech isn't cursing by traditional definition, but it will cause fists and bullets to fly just the same. Religion, politics, social class, and wealth are touchy subjects - as is mention of the Unification War.
Frontier Slang
In English, there are two predominant speech patterns. "Core Speech" is carefully used and grammatically correct. "Frontier Slang" sounds sloppy and quaint to Core speakers, who judge the speaker as poorly educated and low class. Those born outside the Core are more likely to have at least a little of the Frontier in their speech.