Second-person Point of View
Games using a second person perspective provide an on-screen "you," an avatar which the player controls within the game world that is visible to the player through the game's view. Second-person Point of View tends to appear in games that focus player control on a single entity, which helps establish a sense of player identification with the entity where the perspective and manipulation are co-joined.
See also Locus of Manipulation, Single Entity Manipulation
Strong example Super Mario Sunshine [Koizumi and Usui, 2002] provides a player avatar in the form of Mario, plucky plumber and (for this episode) cleaner of graffiti. The game provides the player with a view of the game world that follows Mario such that he is always on screen, typically in the center of the lower third of the screen.
Strong example Baten Kaitos: Eternal Wings and the Lost Ocean is an example of second-person POV because the game is seen through the eyes of a spirit (the player) who accompanies the game's protagonist throughout his adventures. The spirit communicates with the protagonist, Kalas, and even has the chance to attack occasionally, but the player controls Kalas. Furthermore, the player sees the world through the eyes of the spirit and only knows what the spirit knows.
Koizumi, Y. and Usui, K. (2002). Super Mario Sunshine. Nintendo, gamecube edition.