That is efflorescence: mineral salts left behind as water moves through the concrete or block and evaporates on the inside surface. It is harmless itself but it is proof that water is moving through the wall, which means a moisture problem worth addressing.
More detail
Efflorescence is the white, chalky, sometimes crystalline residue that appears on basement concrete and block walls (and sometimes the floor). It is mineral salt, specifically the soluble salts that are naturally present in concrete, block, and mortar. Here is the mechanism and why it matters: water moving through the wall from the wet soil dissolves these salts, carries them to the inside surface, and then evaporates, leaving the salt deposited on the wall face. The efflorescence itself is harmless and not mold (a useful distinction, since homeowners often fear the white residue is mold), but it is unambiguous physical evidence that liquid water is migrating through your foundation wall. In other words, efflorescence is a symptom you can read: where you see it, water is moving through the wall at that spot, even if you have not caught the wall visibly wet. In Cincinnati it is extremely common on block and stone foundations because those materials are more permeable than poured concrete. Wiping or brushing it off does nothing about the cause; it will return as long as water keeps moving through. The right response is to treat the moisture, not the residue: depending on whether the water is hydrostatic seepage or vapor, that is interior drainage, encapsulation, or both, the same solutions that address any Cincinnati basement moisture problem. We use efflorescence patterns during the on-site assessment as a map of where water is actively moving through the walls, which helps confirm the source and scope the system. If efflorescence is the only symptom and the basement is otherwise dry and not humid, it can indicate a relatively low moisture load, and we will say so rather than overbuild; but it should never be ignored as merely cosmetic, because it is the wall telling you water is getting through.