What is Quantum Cryptography?
Today's "normal" cryptography relies mostly on mathematical principles. For example RSA is based on the practical difficulty of the factorization of the product of two large prime numbers, the so-called "factoring problem".
Quantum cryptography (quote from Wikipedia):
Quantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks.
So instead of relying only on mathematical principles, quantum cryptography relies more on quantum mechanical properties (physics). Some of these properties include:
How secure are data that encrypted with Quantum Cryptography methods?
Quantum cryptographic tasks (often incorrectly called quantum cryptography) are theoretically 100% secure, even against quantum-computers.
The method described in your question is Quantum key distribution (QKD). QKD has provable security based on information theory, and forward secrecy. This is based on the No-cloning theorem, which states that it is impossible to create an identical copy of an arbitrary unknown quantum state.
EDIT: This answer provides some additional information.