Background, I'm not an electronics engineer but as a kid assembled a lot of Radio Shack (number) in One kits. I work in IT and have been using a computer since age 5. I would say on a high level near expert on computer hardware, but on the modular level, not component level.
Basically what the Arduino has taught me about electronics is:
The things that I always thought were hard are actually easy.
The things that I always thought were easy are actually hard.
Meaning that a lot of stuff you just plug 2 or 3 wires into it, and go straight to the pins and it works.
The hard part is wrapping my mind around things like taking a 2 pin component and then piggybacking a resistor across it in parallel for some particular reason.
My mind can't really comprehend taking resistors across power sources. I keep thinking, the resistor is causing some kind of short and is going to either heat up or eat the battery.
Also before the Arduino, I had never used all 3 pins in a potentiometer. I always went just two pins, middle and left. I think I sort of understand what using 3 pins is doing... Pulling a pin up or down rather than just down vs "not down" it makes sense now that I understand that pins on integrated circuits can or will float when not pulled up or down.
I really had thought I understood voltage vs current, but I would say only the very basic aspect of it. Arduino has taught me there's more than I thought. Voltage is sort of pushed, current is drawn. A .5 amp light bulb is not necessarily going to explode if it's on a 100 amp source if the voltage is the same as long as it is working correctly. If it fails or shorts internally then yes it might blow up but that's when you need a fuse or circuit breaker.
Can you imagine what the American space program would have been like if you could have gone back in time to the beginning of it and handed them a box full of Arduinos and a method of programming them and basically said "These are what all the pins do, this is the programming language, don't ask how it works, it's all top secret." ?