Various molecules have what amounts to mechanical resonances as the atoms in them have mass, and the bonds between them act as springs. In other words, the atoms in a molecule can vibrate around the whole thing's center of mass if "pinged" by some energy at the appropriate frequency. For this picture, the old ball and stick model is relevant. These frequencies tend to be lower than those of visible light (in general), and most (but not all) covalent bonds tend to have a preferred "angle" that things come to rest at, which is what defines the shape of a molecule. The qualification above allows for things like "folding" in proteins etc.
A complex molecule can have several different resonant frequencies, depending on which bonds are being bent during the vibration, how strong they are, and how much mass is hanging off either end of a bond. It's a bunch of spring-mass harmonic "tuned circuits" floating in space.
Terahertz frequencies are above most radio waves, yet below most infrared. Radio waves, IR, visible, UV, X-rays - all are photons, here given in ascending order of how much energy is in each. Frequency is a measure of energy per photon, though there are other ways to specify that, for example, you can use energy (usually in electron volts) instead.
Calling it a laser, well, that's just a method to produce photons that are all in phase (coherent), there are a lot of ways to get that - a simple RF transmitter produces all-in-phase waves as well - the distinction here is how they get produced, and there are lasers that can be made at almost any frequency. Laser stands for "light emission by stimulation of radiation", MASER is the same thing but for "M=Microwaves". These are done by getting a whole bunch of atoms in the lasing media "pumped up" into states above the ground level energy, which will then "fall back" to a lower state when another photon of that same energy difference goes by, and create another photon of identical characteristics. In the higher energy state, what's going on is that one or more electrons in the lasing media has somehow been pumped up to a higher orbit, and letting it fall back down to a lower state supplies the energy to create a photon -
For reference, visible light has an energy range of about 1.4-3 electron volts per photon, right in the range of various low energy chemical reactions/atom, which makes a sensor for it (your eyes) pretty easy to do in biological tools. Energies higher than that (UV and up) are called ionizing radiation because a photon can actually knock an electron off an atom or molecule - those we consider somewhat dangerous. Below that (eg cell phones, microwaves etc) we don't consider them harmful (except for the usual fringe tinfoil types), as they don't have enough energy to do that.
At any rate, if you make a pulse of terahertz energy that is broadband, and then listen to what comes back over time - you get a complex return signal that indicates the resonances of the stuff you hit with the pulse, one way of doing this. Another way would be to sweep the THz signal over a band and look for absorbtion resonances frequency by frequency - they're not saying which they are doing here.
The way these photons interact with matter is that matter has positive (nuclei) and negative (electrons) that aren't exactly co-located - molecules are somewhat "polarized", so a little packet of electromagnetic energy (a photon) can impart (move around) those charges in relation to one another, which results in mechanical motion.
Here's a table of the usual range we work with photons in, with frequencies, wavelengths and energies characteristic of the various "bands" we divide them into for easier reference:
http://en.wikipedia.org/wiki/File:Light_spectrum.svg
And here's the article (more than most want to know I suspect).
http://en.wikipedia.org/wiki/Electromagnetic_radiation
