What is this dark stain on my flooring and can I fix it?
There are three possible ways to fix this.


Drying, sanding, bleaching, re-staining to match the existing stain, apply clear coat. This option requires that you are able to match the new stain to the color of the rest of the floor. There are videos and how-to articles available to explain the details.
Replace damaged boards with good boards. If the existing floor is worn/old even an exact match of new original flooring will be an obvious repair. There is online information for this process.
Replace the whole floor.


I don't think you will be able to do option 1 and get a match that will please your landlord.

There are people who specialize in repairing this type of floor damage. It won't hurt to get an estimate. Google "repair wood floor water damage" and you'll get a list of businesses. Someone with experience might be able to match the existing floor.

If the repairing the floor won't please your landlord you might be able to persuade him/her that the floor is old and nearing the end of it's life and you should only have to pay some percentage of the whole cost of a new floor.

I'm sorry I don't have easier options.