eli5: how do high-voltage mouse traps make 6000+ volts from 4xAA batteries?
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When you swing a hammer, the sudden stop of the heavy head creates a huge force on the nail. Much more than you could create just by pushing.
You can use a similar system with electricity. By flowing electricity through a coil and suddenly shutting it off, you generate huge voltage spikes from the coil. Doing this over and over gives you a voltage that goes up and down, topping out and thousands of times your original voltage. This might already be enough to shock a mouse, although it is likely that this voltage is used to charge a capacitor to store it up shock the mouse much more.
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