A board foot is a volume of wood that is 12 inches x 12 inches x 1 inch.
You can calculate board feet by multiplying the length, width, and height in inches, then divide by 144.
21 x 42 x 1.5 / 144 = 9.2 board feet. The rest is waste from cutting, planing, trimming, shaping, and sanding, plus the excess scraps that you will save for future projects. :-)
Steve's estimate is for a slightly thicker cutting board than the one the OP specified. His estimate for the amount of lumber needed seems reasonable to me.
Another important point:
A cutting board this size weighs a lot. A 21 x 42 x 1.5 inch cutting board made from walnut would weight over 30 pounds (nearly 14 kilograms). My spouse would not want a cutting board that heavy.
(Here is the math, which you can safely ignore: Walnut is roughly 40 pounds per cubic foot. That's 3.3 pounds per board foot. 9.2 x 3.3 = 30.4 lb; = 13.8 kg)