What is up and down conversion in photonics?

In the field of quantum optics "parametric down-conversion" is a process where an intense pump laser shines an optical non-linear crystal and strongly correlated or entangled photon pairs are generated.

In an optical non-linear crystal the polarization response of the material to the optical field is non-linear, which typically occurs at high intensity.

The photons of the pump laser have energy $\hbar \omega_p$ and momentum $\vec{k_p}$ which must be equal to the sum of the energy and sum of momentum for the produced photon pair: $\hbar \omega_p = \hbar \omega_1 + \hbar \omega_2$ and $\vec{k_p} =\vec{ k_1} + \vec{k_2}$. Conservation of the parameters energy and momentum lead to strong correlations or entanglement between the produced pairs. I believe the name parametric indicates the fact that certain parameters are entangled whereas other parameters are not.

The process is not very efficient but the experimental setup is not very difficult and acts as source of entangled photon-pairs in many experiments on the foundations of quantum mechanics addressing the EPR paradox.

Parametric up conversion probably is the reverse process where entangled photon pairs form one new photon - I am not sure however.

I complete Gerard's answer: up-conversion is the reverse process, where two low frequency photons are converted to a single high-frequency photon.

So basically down- and up-conversion correspond to a frequency conversion of the photons through a nonlinear interaction. The up/down term correspond to the "direction" of the frequency change.

I have to add that the "parametric" term has nothing to do with entanglement, but with the fact that the χ⁽²⁾ nonlinearity used is analogue to a classical parametric oscillator http://en.wikipedia.org/wiki/Parametric_oscillator .