That is called efflorvesence, it is mineral deposits that result from moisture coming through the wall. It is fairly easy to remove it, (a wire brush is usually effective), and the wall needs to be painted with a water proofing paint. Make sure the paint you use is specifically made for below grade applications. These paints contain Portland cement and will seal the wall to stop the moisture penetration. I have recently used a new one that was a low odor oil based product {Zinsser Watertite}. This product was unusual because it left a smooth surface rather than the sandy surface other waterproofing paints usually leave.
However, there could be an underlying cause that needs to be addressed: The exterior walls may need to be water proofed, and proper drainage maintained, (not all that hard to do but can be a lot of work), to completely eliminate the problem. The problem is more common with cinder block walls than concrete. because they are more porous.