At the lowest level, everything in an electrical system is either a 1 or 0, represented by a voltage. For instance, an Arduino reads 5 volts as a 1, and 0 volts as a 0. There is a bit of tolerance in the middle as well, both due to the nature of electrical components and to allow for hysteresis in the system. Continuing the Arduino example, it (should) read a signal as low as 2 volts as still being high. But, if you drop lower than that you may get into a weird area. Something that should have been a 1 is read as a 0, for instance. If power is interrupted and the power supply suddenly sags, this can happen.

This can directly cause things to get messed up, or more complex devices will have a watchdog that'll say "hey this incoming voltage is too low, idk what is going on but stop doing stuff" to put the device into a safe mode (so it doesn't do something unintended and stupid when suffering from low power). When the watchdog triggers, the device will enter into a safe (for itself and other connected devices) state, but beyond that how we perceive its functionality can be anything from it being frozen to it just turning off.