Efflorescence

Efflorescence is a white crystalline or powdery, often fluffy/fuzzy deposit on the surface of masonry materials like concrete, brick, clay tile, etc.  It's caused by water seeping through the wall/floor/object. The water dissolves salts inside the object while moving through it, then evaporates leaving the salt on the surface.

It can be relatively easy to remove compared to some other stains. Often these salts are water soluble and, if outside, may disappear of their own accord with normal weathering.  This is particularly true of "new-building bloom."   The water soluble salts can be removed by dry brushing or with water and a stiff brush.  Heavy accumulation or stubborn deposits of white efflorescence salts can usually be removed with a solution of muriatic acid and scrubbing (1 part acid to 12 parts water -- this is a real acid, follow precautions on the label).  Wet the surface well before and after the solution is applied.  

Less common salts, that change their chemical structure during efflorescence formation, require proprietary compounds to remove.

Here's a page about removing and preventing efflorescence.  I include this link for information not for the stuff they sell.  I found them on a random web search so, I know nothing about the products/company.  You can find products locally that do the same sort of things.