Removed front closet doors and hardwood below is a different color
The rest of your floor has been stained a darker color and has also weathered with exposure to air.

You have a few choices of how to handle this, listed here from hardest to easiest:


Refinish the entire floor and then it will all be bright and shiny like that strip. (This will be both time-consuming and expensive).
Find the correct stain to match the rest of the floor and carefully fill in the space, applying one light coat at a time until you have matched the existing color. (This will not be expensive, but it might be difficult to find the correct color, will be time-consuming, and a small mistake making it too dark will probably call for stripping and starting again. You will probably also have to strip a little finish right along the work area because the lines are so sharp.)
(Suggested by @Ack) Strip the existing finish from inside the closet only, then refinish the entire closet floor (including this strip). If it's not the same color, it will look like it was meant to be that way to define the closet space. It should probably be a darker color than the main floor.
Nail a threshold to the floor over the spot. You can get a wood threshold and stain it to match (the floor or the rest of the doorway trim) or deliberately leave it contrasting to mark the edge of the closet, or a metal or plastic one.


If it were me, I'd do option #3 or #4. Since the closet is already an obvious doorway, having some difference on the floor (whether threshold or stain) would not be out of place.