aka "quantum resistant"; refers to cryptography running on a classical computer which is resistant to quantum attacks. For algorithms running on a quantum computer, see [quantum-computing].
It is widely know that quantum computers (specifically Shor's algorithm) break our current public-key crypto systems based on RSA and elliptic curves. This includes public key encryption, digital signatures, and Diffie-Hellman key exchange.
Academics are heavily researching alternative public key systems which are resistant to attacks from both classical computers and quantum computers. This field of research is called "Post Quantum Cryptography" - often abbreviated as "PQCrypto".
The list of mathematical techniques that could yield successful post-quantum crypto primitives includes, as of writing May 2016: