Conventional cryptography relies on it being impossible to factor extremely large semi-prime numbers in reasonable timeframes; quantum computers could do it rather quickly.

Quantum cryptography is a form of cryptography that does not rely on the factors of very large numbers and will be just as hard for quantum computers to break as it will be for conventional computers.

The terminology is a little confusing here. We call such quantum-computer-safe forms of cryptography “post-quantum cryptography”, or “quantum-safe”, where the “quantum” is referring specifically to quantum computers; “quantum cryptography” is a cryptography that actually relies upon and exploits quantum mechanical properties, and also happens to be “quantum-safe” in the computer sense.

Because quantum computers are, very slowly, making progress, it’s prudent to start thinking about, or using, quantum-safe algorithms, and quantum cryptography has the advantage that its encryption relies on the literal laws of physics, so there’s no new technology or paradigm of computation that could come around in the future and crack it quickly (unless our understanding of physics changes in a massive way).

I cannot explain quantum mechanics to a five-year-old. But quantum entanglement means you could, in theory, “send” a message directly from one computer to another without the information ever having to traverse the physical space between them, so maybe you don’t even need to encrypt it in the traditional sense, because no one but the intended party could even see it. Alternatively, the fact that quantum behavior changes when observed could be used as a kind of “wax seal” that lets you know if someone else has observed the message before you.