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.
If Quantum Computing becomes practical and is mass-produced, will we be facing with next-generation of cybersecurity?
Not necessarily. I personally think that quantum computers won't fully replace classical computers, because quantum computers only outperform classical computers in certain areas (i.e. large-scale simulations).
But if quantum computers were available they would break some of today's cryptography used on classical computers, i.e. RSA or Diffie-Hellman. We would then have to switch to post-quantum cryptographic algorithms like Supersingular isogeny key exchange. So ultimately, I think, we would just switch to quantum-resistant algrorithms and go on with our lives.
EDIT: This answer provides some additional information.