What do they mean by MOD 6?

It's the remainder of integer division by 6.

If you recall way back in grade school when you were learning division you were taugt the report the quotient and a remainder. That remainder is the modulo

15 mod 6 = 3

because

15 = k*5+3

It's very useful for detemining if one number is a divisor or another:

when

n mod k = 0

that means that n is an integer multiple of k

MOD is like division, but only returns the remainder.

For example, 14 mod 3 return 2.

That is because 14 divided by 3 is 4 with a remainder of 2

It's short for modulo. See link below.