What does as a product of prime factors mean?

Answer 1

That's asking for the prime factorization. Writing 60 as a product of its prime factors would be 2 x 2 x 3 x 5 = 60.

Answer 2

It means that an integer is split into smaller integer factors, until all the factors are prime numbers. For example, 12 "as a product of prime numbers" is equal to 2 x 2 x 3.