Oh yeah, most likely mold and the wood beneath it will be rotting if not already as well as the walls. Absolutely get someone to look at that and fix the water leak.

How is something like this repaired?

It depends where the water is coming from. Are your gutters clean. Are the downspouts clean of debris, and draining properly, and are they running away from the house. Does your roof have a leak, or a window have a leak, that is running inside the wall, and out at the bottom and running into the area, where you have the stain? All things to check. Please roll the carpet back, and get it dried out, and if there is mold there, get it cleaned up, so you and your family or pets are not breathing it. Once it is dried out, leave the carpet off that area, and watch and maybe you can see where the water is coming from. Is there a water pipe underneath there, that is spraying up on to your sub floor? Or are you on a concrete slab?

Not sure if this is a real thread. I would submit that anytime it rains, all the outside becomes wet.

What I see there is someone eats at a desk, and spilled a drink and some crackers. Decades of experience with tenants leaving that exact same pattern behind, that actually might be one of my pictures.

You would have to give much more information to find the correlation and cause for water entering from outside.