What does "express each number as a product of its prime factors" mean?

Well a product is what numbers multiply to get another number.

For example 3 and 2 are products of 6, because 3 x 2 = 6

And a prime number is a number with only 2 factors (I'm assuming you know this already)

So if you wanted to find the prime products of 24, you would do so like this ...

24 = 12 x 2 (2 is a prime so that is ok, but 12 is not)

So then you ask what numbers are 12 made of?

24 = 3 x 4 x 2 (2 and 3 are primes but 4 is not. So you do as before)

24 = 3 x 2 x 2 x 2 (All the numbers are primes so you have finished)