If we draw a line using a ruler on an $8\times8$ chess board, what line can touch the most squares, how many? Is it the diagonal?
Maybe this image which presents a line crossing through 15 squares on a chess board might demonstrate or at least help your understanding of the answer.
As you can see, a slightly offset diagonal line fully enters 15 squares in an alternating pattern. And yes, this is the line which touches the most chess squares (or at least one of them).