COLUMN(C13) returns the column number of cell C13, which is 3. Subtracting 3 from that gives you 0 and passing 0 as the column argument to INDEX gives you all the columns of the relevant row.

The QUOTIENT function returns the integer part of a division, ignoring any remainder. SO that part is taking the row number, subtracting 14, dividing by 31 and keeping the integer part. You then add 3 so the result here will never be less than 3.
Other than the first block of 3s, you will get blocks of 31 of the same number - i.e. 31 4s followed by 31 5s and so on.