I think an important concept to introduce is Pulse Width Modulation, or PWM for short.
Normal AC Power coming out of wall looks like a sine wave, in that it smoothly cycles between +110/240V and -110/240V. This means that 50% of the time the voltage is positive and 50% of the time the voltage is negative.
PWM usually deals with signals which are either entirely on or off, with no transiton between them. This way, you can vary the amount of “power” delivered by varying how much of the time the signal is on and how much of the time it’s off.
Dimmers usually modify the sine way in a way that tries to accomplish the same thing, by chopping up the signal to make the effective “on” time be shorter than 50%.
With non-dimmable LEDs, this messes with the AC to DC circuitry in the lamp in the way slazer2au says, because the lamp doesn’t retain enough power between two on-cycles to stay on.