Why is it that photons are emitted in bundles?
My physics teacher's answer was "it's complicated"...
Photons aren't complicated, Instead they're non-sensical! This topic is really about "Quantum Weirdness."
First let's get one thing straight: photons are not emitted in bundles. Instead atoms emit photons one at a time.
I'm guessing here, but I think the teacher was trying to communicate the following: EM wave-energy is emitted and detected as photons. This could be translated as "Light is emitted in bundles called Photons." Each photon is something like a bundle of light. So, the OP question is probably not about bundles of photons. It's about photons themselves, where each photon is a "bundle of electromagnetic energy."
But don't forget that this topic is non-sensical. You cannot visualize photon behavior. Nobody ever has. Light is waves which are particles, and the infinitely small particles are waves at the same time. It's like trying to visualize a square circle, or dark whiteness. The experts get part-way there by using many different ideas. Something here is very complicated: the ideas being used to explain photons. Ideas such as instantaneous wave-function collapse, or multiple-universe splitting in the Everett-Wheeler Many Worlds theory. Richard Feynman's QED assumes that each atom emits an infinite number of "virtual" photons which take all possible trajectories, then they combine together to form one photon which impacts an atom.
Some good books:
Taking the Quantum Leap, by Fred A. Wolf
Shrodinger's Kittens, by John Gribben
QED by Richard Feynman
In general photons are emitted one by one from individual atoms.
I suspect you were discussing laser photons, and also suspect that you still are in high school. Photons from lasers do come in bunches, and your teacher is correct that it is not simple to explain it. Let me try.
Have you seen the domino set ups, where the tiles are finely balanced and then the first one is pushed and all the rest start falling in steps?
In lasers the atoms are artificially pushed up to an excited state, and when a photon of the right frequency passes, the atoms fall to the lower state all in step and thus appear as bunches.
I'm going to go out on a limb here. Maybe your teacher was referring to "photon bunching", which is often described as a tendency for photons to be emitted in bundles. (If this is not the case, ignore what follows!)
Photon bunching refers to the statistics of the arrival time of photons as you would see them at a detector. Photons from a noiseless laser will be detected randomly, according to a Poisson distribution. On the other hand, photons from a thermal source such as a light-bulb will also be detected at random times, but according to a Maxwell-Boltzmann distribution. A peculiarity of the thermal photon statistics is that the conditional probability of detecting a second photon immediately after a first is higher than at later times and is thus bunched. For the laser, the probability of photon arrival is uniform at all times. In contrast, light from a single emitter (such as an atom de-exciting from its first excited state) can only emit one photon at a time before having its electron re-excited, and thus has a decreased probability of having a second photon present. Hence this would be anti-bunched light. If you're interested, the relevant terms for the quantum states of light of thermal, laser, and single photon sources are Thermal state, Coherent state, and Fock state respectively.
Otherwise your teacher probably meant that photons are detected as discrete packets of energy as was explained above.
An atom emits a photon when an electron moves from a higher energy orbital to a lower energy orbital. The energy difference between the two levels equals the energy contained within the "bundle" or "packet" of energy known as a photon. Most light sources have many atoms, any of which may emit a photon, thus resulting in many photons or "bundles." In defense of "bundles of energy" (since this is now at -1) read the top answer here.