Surface water is saturating the exterior foundation wall. When the (liquid) water evaporates what is left is mineral deposits that create the stain. The mineral deposits seldom if ever cause any problem at all. They can be washed off however it is simply not worth the effort. Many times the minerals will require use of an acid solution, not something anyone in their right mind would ever want to use inside of a home without adequate ventilation.
Home inspectors use fancy terms like correcting problems with surface water controls. What we mean by that is to get surface water to drain away from the home using any method available. If surface water is not directed aggressively away from the home it will saturate the soil, soak down till it hits the virgin soil near the level of the footing. Surface water that can not soak further down accumulates pushing through the foundation wall and or the basement floor causing water infiltration issues.
In all cases failure to make immediate improvements to surface water controls must be expected to result in water infiltration and the possibility of very expensive to cure structural damages. Surface water saturating the soil against the foundation walls has been known to freeze, expand and push the foundation walls in. It is NECESSARY to regrade the soil around the perimeter of the home to encourage surface water to drain away from the foundation walls. Surface and or roof water that does not drain away from the foundation must be expected to result in water infiltration and damages. Remove debris from gutters and downspouts regularly and configure their discharge so they effectively discharge water at least 10 feet from the home. Even if the homeowner represents water infiltration did not occur yet or the grading defect existed for years or comes up with any other plausible excuse, immediate corrective actions are still necessary in order to avoid further problems and damages.