Sindarin is one of the two main Elvish languages Tolkien created. It's the language of the Grey-elves, who lived in the regions of Lindon and Lothlórien, and was the language of the elves of Beleriand before its destruction.
Here are some examples of Sindarin words used in the books:
* Arwen Undómiel: Her name itself is Sindarin, meaning "Noble Maiden" (Arwen) and "Evening Star" (Undómiel).
* Lórien: The name of the land of the Golden Wood, meaning "Flowering Wood."
* Celeborn: The name of Arwen's father, meaning "Silver Tree."
* Elbereth: A name for the Valar Varda, meaning "Star-kindler."
While Arwen would have been fluent in Sindarin, she would also have been able to speak other languages, such as Quenya, the High-Elven tongue, and likely some of the languages of Men.