What does decompose into their prime factors mean?

Decomposition means to break down. All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.
Example: 210

210      Divide by two.
105,2     Divide by three.
35,3,2      Divide by five.
7,5,3,2       Stop. All the factors are prime.

2 x 3 x 5 x 7 = 210
That's the prime factorization of 210.