Books that explain DSP well to those not directly in engineering?
I am surprised no one has mentioned Richard Lyon's book - by far one of the BEST books out there on understanding digital signal processing in a very clear, concise, and methodological way. 

Its excellence comes from that fact that he explains concepts to you in a very easy way to grasp, without loss of rigor or detail needed to get to the heart of various DSP concepts. He does not shy away from math, (which is good), but you are guaranteed to understand all of it.