When the inspector did the check out of the house he mentioned the basement
foundation had evidence of water problems. We talked about it with the
seller and agreed that his fix prior to selling was adequate for my
purposes. Anyway, the inspector pointed out these chalky deposits on the
concrete walls of the foundation and that he sees this all the time with
water problems. It looks exactly like chalk or lime is sitting on the
surface of the concrete and if you poke at it the white chalky substance
flakes off.

I guess my question is, what is the white chalky stuff? The inspector said
something akin to the concrete materials were leaching to the surface,
calcification I guess.

As a follow on, assuming the water problem has been resolved does the
presence of the chalky stuff on the concrete indicate that I don't have a
hope of sealing my basement against further water, should the problem come
back in the future? The original owner put down a tarpaper, 2x4, plywood
floor on the foundation as the flooring material and I'd like to remove it
and put down something a bit more roomy - like all-weather carpeting or
tile.