Ithilien, whose name means "Land of the Moon," is described by Tolkien as "the garden of Gondor." Geographically, it is the long strip of land across the river Andúin from Gondor that lies between Gondor and Mordor. Because of its location, it is strategically favoured by both kingdoms.
We are first introduced to the Ithilien when Frodo and Sam encounter Faramir there (Faramir's hideout at Henneth Annûn is located in the heart of Ithilien).
After the War of the Ring, Aragorn reclaimed the throne of Gondor, basically leaving Faramir without a job (since Gondor has been previously ruled by Stewards and Faramir was the last of them). Aragorn honored Faramir by giving him the land of Ithilien to rule as Prince (in much the same way as Imrahil, Faramir's uncle, ruled Dol Amroth).
Faramir and Éowyn took up residence in Emyn Arnen, a hilly part of Ithilien just to the southeast of Minas Tirith, and lived out their days there together.