This would be easier to explain with a whiteboard, but I'll give it a try.
First, you need to know a few things about molecular potentials for diatomic molecules. You have a look at
http://hyperphysics.phy-astr.gsu.edu/hbase/molecule/molec.html, under Molecular Spectra. Just like atoms, molecules have many electronic states. The energy depends not only on the electronic state, but also on the interatomic distance
R. Stable molecules are formed because the potential energy curve has a minimum that can support bound states. When the molecule is in a given vibrational state, it is stable to dissociation: energy needs to break it so it is above the dissociation energy (indicated on the figure), as the energy goes asymptotically to a certain value as
R→∞. Conversely, if you start from two separated atoms, a collision corresponds to
R→0. Unless there is a mechanism to take away energy (most often a three-body collision), after collision you have two individual atoms as
R→∞ again.
In many diatomic molecules, that single electronic ground state is actually degenerate (for instance because of hyperfine interaction). A magnetic field lifts this degeneracy, and the result looks like https://www.researchgate.net/profile/Andrey_Miroshnichenko/publication/24013351/figure/fig12/AS:272575829901313@1441998550232/Figure-7Color-online-Two-channel-model-for-a-Feshbach-resonance-Atoms-that-are.png. Note that the splitting between the purple and the red curve depends on the strength of the magnetic field. Starting from two separated atoms with the energy of the green line are in the electronic state given by the red curve. When they collide (
R→0) if the difference between the collision energy and a bound vibrational state is small, the system can end up in that bound vibrational state. The molecule formed is not stable, and decays back to the red electronic state and the atoms fly apart. However, that momentary transformation to a bounb molecular state has observable consequences and is called a Feschbach resonance (for a fixed collisional energy, as the magnetic field is changed, there will be a resonance when a bound state coincides with that energy).
Each electronic state is called a channel, and open channels are those such that the collisional energy is greater than the dissociation energy, while closed channels have potential wells at that energy. You can also think of the process in reverse: starting with a molecule in a bound state of the purple potential, it will vibrate there a while (the channel is closed to dissociation), but eventually it will transition to the red electronic state and dissociate (the channel is open to dissociation).
I'm not sure how microwaves enter in the research concerned, but hyperfine transitions in atoms are usually in the microwave part of the spectrum. Likewise, the splitting between states due to the magnetic field that is responsible for the Feschbach resonance can implicate transitions in the microwave (although it is most often in the radio wave domain).
An optical dipole trap is created using an intense laser that is off-resonance (red detuned) with respect to an atomic transition. An atom interacting with this laser will have an energy that goes down as the intensity of the laser increases, due to its polarizability. By creating a spatially inhomogeneous beam (for instance, by focusing), the atom will be attracted to the high-intensity region and can be trapped there.