I'm trying to understand this sentence (from this answer):
So if your application has high ripple current and you don't need the ESR zero for stability then a low ESR cap will likely be the way to go.
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Without the equations (like you're 5), an ESR zero 'speeds up' the response, that is it reduces the phase shift, around the feedback loop, and so allows you to make an unstable loop stable.
Consider a sudden step of current into the output capacitor.
With a pure capacitance, no ESR, the output voltage will start to ramp, as the current gets integrated.
With a capacitor with some ESR, Equivalent Series Resistance, the current flowing in the resistance will give an immediate step change in voltage, which is then followed by a voltage ramp as the current gets integrated.
It's this immediate step in voltage that makes the loop behave 'better' for stability, although it's worse for output ripple (you win some, you lose some).
It's called a zero because when you do the maths properly (like you're 20), and form an expression for the gain of the regulator, the term containing the ESR is on the top of the gain equation, so when that term goes to zero, the whole gain does. Most other terms, the poles, are on the bottom of the gain equation, and when they go to zero, the gain becomes infinite and you get oscillation.
Why it matters has to do with accidents of history. The original single IC regulators (like 780x) use emitter follower output stages, which are fast and low impedance, but have a large dropout voltage. This was when the only large caps available were aluminium electrolytics, with a high ESR. Low impedance output and high ESR cap meant rock solid stability without much trying. Then people wanted LDOs, so a common collector PNP stage was used for output, which is a slower device with a higher output impedance. Tantalums became available, with a lower ESR than alli, but it was still non-zero. We could still get stability by specifying a minimum ESR and a particular capacitor range. Then big value ceramics appeared, smaller and cheaper than tants. These had (to all intents and purposes) zero ESR. LDOs used with them would sometimes oscillate, not always, but often enough. Stability was not always compromised, but was no longer ensured. The worst problem was when the prototype worked on the bench, and then a new batch in production failed, very expensive to fix. Manufacturers tweaked their designs, prohibited ceramics in the data sheets, but users kept getting it wrong and building oscillating regulators. This gave LDOs a bad name, and put an aura of magick around the output capacitors. Eventually, regulator manufacturers accepted the problem and designed a new regulator topology which assumes the worst case zero ESR output cap, and handles the stability properly inside the regulator. These are marketed as 'stable into ceramic' or 'AnyCap' regulators.
Poles and zeros are concepts from filter design and or control systems. I don't think I can explain how they work to a 5 year old, but the basic idea is that poles and zeros occur at inflection points in the gain of the filter. For example if you have a simple low-pass RC filter, the cutoff frequency is the POLE of the filter. The simple RC filter only has one pole, but more complicated filters can have more poles and zeros. The frequency of the pole in a simple RC is 1/(2*piRC).
Voltage regulators are actually control systems. They attempt to control output voltage in spite of varying input voltage and varying load current. Since they are control systems, they can be unstable under some circumstances. The series resistance of the output capacitor may effect that stability.
So the sentence you are asking about is saying that unless some relatively high ESR is required to maintain stability of the regulator, you are better off having lower ESR because it will lead to lower output ripple voltage.
I hope this makes some sense. Not an easy thing to explain to someone who has not studied it a bit.