Relatively prime means the two numbers do not share a common factor (other than the number 1). In other words, two numbers are relatively prime if when forming a fraction out of the numbers, the fraction is in lowest terms.
Example: 8 and 15 are relatively prime.
8 = 2 * 2 * 2 15 = 3 * 5
8/15 is a fraction in lowest terms
Example: 9 and 12 are NOT relatively prime
9 = 3 * 3 12 = 2 * 2 * 3
9/12 is not in lowest terms. (the common factor of 3 can be cancelled out, reducing the fraction to 3/4)