"Firefly" was doomed from the start since Fox aired the original episodes out of order (and didnt even show the last three). Luckily it built a fiercely loyal fan base that is still active today. They are known as Browncoats (named after the rebel group that Mal and Zoe fought with). "Firefly" is often listed at the top of many sci-fi "best of" lists.
Humans (interestingly there are no aliens in this world) speak a hodge podge of English and Mandarin. They often curse in Chinese. English words are used in novel ways. "Shiny" for example means great or cool. "Gorram" is a curse word. "Old West" terms are also sprinkled throughout.
There are eventually 9 people aboard the Serenity. We met Captain Malcolm "Mal" Reynolds (Nathan Fillon of "Castle"), husband and wife duo Wash (Alan Tudyk) and Zoe (Gina Torres). Mal and Zoe served together during the Unification War so they're very tight. There's a young girl named Kaylee (Jewel Staite) who is the ship's engineer. Jayne (Adam Baldwin) is a surly guy who cant be trusted. He does love his gun Vera though.
Inara (Morena Baccarin of "Gotham" and "V") is a "companion" who rents one of the ship's two shuttles. Companions are part Geisha and part hooker. Prostitution is legal in the future. Inara is very cultured and has many wealthy clients. Inara and Mal have a thing for each other but neither will fess up to it. He calls her a "whore" and she calls him a "petty thief".
To make ends meet, the crew picks up some passengers for transport. They include a Shepherd (similar to a pastor) named Book (Ron Glass) and Dr Simon Tamm (Sean Maher). Simon's cargo turns out to be his sister River (Summer Glau). They are fugitives. River was being experimented on in a government facility. Simon rescued her. River has mental problems and some psychic abilities. She keeps repeating "Two by two, hands of blue".
During one of their planet stops, Mal ends up with a "wife" named Saffron (Christina Hendricks of "Mad Men"). She turns out to be quite the con woman and has at least three aliases-- Safron, Yolanda and Bridget. They meet her again at various times. She and Mal's relationship provides some comic relief.
Other episodes take them to various locales as they attempt to stay away from the Alliance and keep River out of trouble.