The concept of two-dimensional game is putting all objects in a plane; the z coordinate represents depth, which will not be considered in this scope. Knowing this, all your game graphics are expected to be on a plane, where the x axis and y axis are only considered. Your game objects can move up, left, down, right, in diagonals, and at angles within the x and y coordinates.
What's the idea? How will the game be played? You may want it to be in the isometric view (http://wikipedia.org/wiki/isometric_projection) or like a side-scroll, in which the game world presented perpendicular to the direction the characters are facing on the screen. The examples of side-scrolling can be found at http://www.giantbomb.com/side-scrolling/3015-299/games/.
Who's playing your game? You can start with your friends and build a game they'll love to play. What genre is your game? You should be able to define what genre your game is; your game can be a combination of one or more genres. Below are...