The answer to 'soffit water stains' is that they are typically caused by water leaking from the roof or gutters. Symptoms include discoloration, mold growth, and water damage to the soffit and surrounding areas. Solutions may involve repairing roof leaks, cleaning and sealing the soffit, or replacing damaged materials.
If the stains are limited and the underlying cause is clear, a homeowner may be able to address the issue with some DIY work. However, if the stains are extensive, the cause is unclear, or there is significant damage, it's best to call a professional roofing contractor to properly diagnose and resolve the problem.