prime is something that is evenly divisble like 4 whereas compsite is something that is not like 17. 1 and 0 are neither
A prime number is one that has no other factors except itself and 1 [Ex: 17 = 17 x 1]
A composite number is one that has factors other than itself and 1 [ Ex : 12 = 2 x 2 x 3 ]
BTW - The Fundamental Theorem of Arithmetic says that every integer greater than 1 can be expressed as a product of primes or is itself prime