It's not so complex. Your 4x8 bi-colour matrix is, in effect, an 8x8 matrix where half the LEDs are red and the other half green. The max chip has 8 "registers" that the Arduino can update. These correspond to the 8 rows or columns of your matrix, depending how you wire up the LEDs. Each register contains 8 bits. Each bit controls one led in that row or column.
0b11000011 is simply a number written in binary. If the Arduino wrote that value to the 5th of the Max's 8 registers, the first, second, seventh and eighth LEDs in row or column 5 would light.