In static fiction, the main character around which the story centres. In interactive fiction (IF), the character which the player (the person at the keyboard) takes control of - also known as the Player Character (PC). Recent IF trends have seen an increase in the separation between protagonist and player, as protagonists have taken on a increasingly well defined character. In the classic text adventure games, from which IF has grown, the player was not expected to play anyone in particular. In Zork and Adventure (two very early games) the PC was completely unspecified - without even a gender, never mind a personality - and descriptions were given purely objectively. The player was expected to identify completely with the protagonist - to imagine themselves in the situation the story put them in. Detective even went as far as to have the command prompt on the first turn read "What will you, the detective, do now?>". As far as I know, none of the commercial games ever broke this mould.
But with the demise of Infocom and its ilk, and the rise of amateur, increasingly experimental interactive fiction, we have seen a move away from this. Now it is common for stories to have protagonists with a very definite character, and the characterless PC is now almost as rare now as the pure puzzle game format is. Of course, this presents quite a challenge for the author, as the player must feel in control of the character while also being give the impression that they are their own person - aims which obviously can conflict. The common approach, which escapes this conflict, is to provide a sense of character through descriptions - rather than being give flat and objectively as in the early works, the prose is filtered through the subjective mind of the character, with their own comments being made part of the description. This is the blending of the roles of protagonist and narrator, and the introduction of the unreliable narrator. This is too common to be worth citing examples, but see the IFart pure puzzleless piece Cove where the author Kathleen M. Fischer notes that she originally intended not to give the protagonist any character, but found the result dull and lifeless - and so she yielded and gave the character a proper back-story and personality.
Less decided is a way of resolving the conflict between player's free will and the protagonist's need to veto actions out of character. Some prefer to allow pretty much any action, and either to adjust the PC's character in accordance with the player's actions (no good examples of this - very difficult to do well) or to weaken the character. But the IF author must always be searching for ways to reduce the number of allowable actions, otherwise things get far too complicated, and character-based restraints provide a handy way of doing this. See Adam Cadre's Varicella, where the protagonist's character is well drawn through his refusal to do all sorts of things on the basis that they are "unseemly", and for an extreme example Stephen Bond's Rameses, in which almost every player action is disallowed in an interesting, character developing way.
One method of character building which works well in static fiction but has yet to be successfully transferred to IF is the internal monologue. Perhaps the appropriate translation would be an internal dialogue - an actual conversation between the player and the protagonist taking place in the protagonist's mind. You see, IF is still a very fertile and largely unexplored art form.
References : Inform Designer's Manual 4 by Graham Nelson; the various works cited above; rec.arts.int-fiction.