A semiprime (or biprime) is the product of exactly two prime numbers — not necessarily distinct. So 6 = 2·3 and 9 = 3² both qualify; 8 = 2³ and 12 = 2²·3 do not.
Semiprimes are the heart of RSA cryptography: an RSA public key contains a large semiprime whose two prime factors are secret. The difficulty of recovering the factors from the product is what protects the key. The famous RSA Factoring Challenge numbers were all semiprimes.
Semiprimes with two distinct factors have exactly 4 divisors; squares of primes have exactly 3 — the only numbers with an odd prime count of divisors that small.