A clear explanation of the difference the Blackmagic Cinema Camera is going to make by making the jump to 12-bit depth.

Which becomes quite clear with math:

The bit-depth simply refers to the different combinations of ones and zeros that is possible (with color images having three channels of bit-depth). The more bits and values possible, the better the final quality will be.

8-bit   — 256 different values 
10-bit — 1024 different values 
12-bit — 4096 different values