What is this material on my interior foundation walls?
Two common types of things are sprayed on basement walls.

What I suspect you have there is a white "waterblocking" coating - something like UGL Drylock (not an endorsement, just an example. I prefer waterbase version) 
(source: drylok.com)
 It can be brushed or rolled, and a vigorous rolling may well provide the spatter you see. It's also becoming common to see sprayed-on polyurethane foam in basements (it's better put on the outside, but if retrofitting, putting it on the inside doesn't involve excavating all around the building) but that's usually a bit thicker and somewhat yellow (plus it's obviously plastic when you touch it.)