Concatenation is a basic operation in computer science. It basically means that you take two strings and jam them together. For example, the concatenation of "bbaccca" and "acb" is "bbacccaacb".
If we let the letter "b" stand for blue and "g" stand for green, we can build different colorings through concatenation. For example, "bbggggbgb" would represent a 3x3 grid with two blue squares followed by a green square in the top row, three green squares in the second row, and a blue followed by a green followed by another blue in the last row.
When we create a multiplication table, we create a multiplication expression for every possible pair of numbers on the borders of the table. Normally, we write the answer to the expression in the table. I'm writing the expression in the table to make my point:
This is a very small multiplication table, but it illustrates the point. We have every pairing of 0 and 1 in this table, which we could transfer to all the colorings of a set of two squares.