"To make to be here again" > "to make something appear in place of something else". A re-enactment brings past events before your eyes again by substituting the stage and decorations for the actual place and actors for the actual participants. A metaphor brings back or summons something in your mind by preserving the structure of relations while substituting the entities.
@scherz0, I think that the problem arises with the (poor) definition of English "represent" that you are using; I don't like "standing in the place of another" at all. A better definition might be: "to serve as a sign or symbol of another such that it brings the symbolized once again (that is, re-presents it) before the mind". This involves the internalization of an external event, which is the mode of operation of signs and symbols. Instead of a physical/external re-presentation of something, the English lemma describes an internal, psychological re-presentation. From that, can you see the semantic connection? You may see, then, that the semantic shift from Latin repraesentare to English represent is not as great as you might have imagined. Inadequate definitions will always lead us astray.