As a noun: Sylvan or Silvan refers to an association with the woods. Specifically, that which inhabits the wood, is made of tree materials, or comprises the forest itself. The term can also refer to a person who resides in the woods or a spirit of the wood.1 In mythology, the term also refers to deities or spirits of the woods.2
The term in English is from the Latin sylvus or silvus meaning "forest, woods." This root is found in place names in the U.S.A. like Pennsylvania (lit. "Penn's woods") and Spotsylvania. The first names Sylvester and Sylva(i)n, and the female name Sylvia/Silvia, are also from the Latin word.
In one book, the following exchange occurs:
"Huge people - beautiful people - like gods and goddesses and giants. Hundreds and thousands of them, closing in behind us. What are they?"
"It's the Dryads and Hamadryads and Silvans," said Trufflehunter. "Aslan has waked them."
In J. R. R. Tolkien's Middle-earth books, there is a division of Elves residing in forested realms referred to as Silvan Elves.
In the "Age of Mythology" a special power up is awarded to centaurs called "Sylvan Lore". It gives centaurs 25% more hitpoints and 30% more speed.
In Dungeons & Dragons, Sylvan is the language of all magical creatures associated with the wilderness, such as fairies, dryads etc.
In Heroes of Might and Magic V, Sylvan is a playable faction, featuring the Elves and other mythical forest creatures.
In the trading card game "Magic: The Gathering," the term sylvan appears.
John Keats calls the subject of his famous poem "Ode on a Grecian Urn" a Sylvan historian.
In Christopher Hill's book "The World Turned Upside Down" the term Sylvan refers to "wild men" - people of the forest. They retreated to the woods away from the city because they disagreed with the laws.
In "Dragon Age: Origins," the player's party battles living trees known as Sylvans in the Brecillian Forest.