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.
Well maybe I can help with a better 'pot' explanation.
First there are available two terminal variable resistors called a rheostat (that's probably a brand name) that by moving the knob you can change the wiper pin to the other pin's resistance from 'zero' ohms and whatever the devices maximum resistance value is, say 10K ohms. A pot (potentiometer) is a three terminal device that has a third pin that is called the wiper terminal. If you wire the wiper terminal to one of the end terminals you will have converted your potentiometer to be a two terminal rheostat control. But by using all three terminals on a real 3 terminal pot one has the ability to form a voltage divider with a movable output voltage equal from ground to whatever voltage is applied to the other fixed terminal, which is a very useful function used in many circuits.
The first major milestone to getting a real good start in understand electronics is to really master ohm's law. And by master I don't mean to just memorize the three basic formula that make up ohm's law, E=IxR, R=E/I, and I=E/R, but to really understand what that means and how it defines the interrelationship and interdependency of voltage, current, and resistance with each other. Without that true understanding it makes moving on to the more complex fundamentals of electronics all the more difficult. Electronics is really not a rule based subject based on pure memory of such rules, but rather the understanding and application of fundamental principles into practical components and circuits.