Generally speaking, fan service is simply "giving the people what they want."
Xena and Gabrielle sharing a moment of subtext, Trowa and Quatre from Gundam Wing playing music together, the lovingly detailed footage of Voltron forming, or a random yet popular redshirt or bridge bunny suddenly getting lines... Fan service, all of it.
Arguably, the Evangelion movie is an example of fan service for people who dislike fanboys.