What are the mechanics behind atoms and molecules emitting infrared? The usual explanation for discrete spectra is that electrons can absorb particular wavelengths of the electromagnetic spectrum, move up to a higher energy level, and then electromagnetic waves are released when the electron moves back down to its original energy level. I read that an electron in a particular subshell must have a particular amount of energy which can't vary, and I've also read that this electron jumping explanation is not what happens when atoms and molecules emit infrared radiation.
I've read that anything above 0 kelvin emits infrared. Apparently infrared absorption doesn't excite the electrons, but changes rotation, vibration, etc. What I don't understand is the mechanics behind what causes the infrared to be emitted in the first place (is it somehow related to electrons like the explanation in the first paragraph?), and why specific wavelengths of infrared lead to emission which can be used to identify substances
 A: 
I've also read that this electron jumping explanation is not what happens when atoms and molecules emit infrared radiation.

This is not a correct statement. Electron "jumping" or electronic transitions cause atoms to emit at wavelengths in infrared region(Paschen series of H atom). Of course there are other possible sources as:
Rotational spectra: The rotation of molecules about it's bond is quantised. So going from one rotational state to other can cause the molecule to emit infrared radiation.
Vibrational Spectra: Like the molecule can rotate around it's bond, the bond length also is not an constant. Rather in can vibrate and different states of vibration has different energies associated to it. Transitions between these states can cause infrared radiation.
A: In my view, particularly for IR transitions, the picture of electrons "jumping" is not very helpful. My favored explanation involves treating electromagnetic radiation as a classical field, and the energy levels of the atom or molecule as quantized – a very reasonable approximation for IR light, since its wavelength is much longer than the size of an atom or molecule. This is called the electric dipole approximation.
As you know from classical electrodynamics (and from everyday experience with radios and cell phones), an oscillating electric dipole emits radiation. Atoms and molecules obey the same rule. In their case, however, the oscillating dipole in question can be viewed as the superposition of two states with different charge distributions. The probability distribution for the charge of an atom or molecule will oscillate in time with a frequency equal to the energy difference between the two levels in question. They can be different electronic states, vibrational states, or rotational states, all of which are quantized, as mentioned by Ari. The superposition "lives" for a certain amount of time, and the atom or molecule emits a wavepacket of radiation with a similar temporal envelope. 
Of course, you run into trouble when you think too hard about the fact that for any single atom or molecule, what's oscillating in time is the probability distribution for the charge, not the charge distribution itself. But when considering many atoms or molecules, this distinction becomes unimportant.
