We just used a 10,000 ohm resistor and a 10,000 ohm thermistor to divide the 5 volt power supply in half, to roughly 2.5 volts, varying with temperature. If we wanted a steady source of 2.5 volts, we could use two simple (and cheap) 10,000 ohm resistors, and measure the voltage between them. If we wanted a steady 1 volts source, what resistance would we connect to 5 volts, and what resistance would we connect to ground?
A potentiometer is a three terminal resistor. One terminal connects to the input voltage (say 5 volts), and another connects to ground. A third terminal is connected to a "wiper" that contacts the resistive material between the two ends, forming a variable voltage divider, allowing us to select any voltage from zero to the full input voltage. What could we use such a device for?
The tiny computer can use either 5 volts, 3.3 volts, or 1.1 volts as a reference for measuring voltages. Using the 1.1 volt reference (see the analogReference() function), we can measure voltages as low as 1.1 volt divided by 1024, or 0.00107421875 volts. That's 1.074 millivolts. But what if we wanted to measure voltages above 5 volts? How would you use a voltage divider to measure voltages between 0 and 11 volts?
Ohm's Law tells us that we can use a voltmeter to know how much current is going through a resistor. It also tells us we can use a voltmeter to measure resistance. How would you turn our tiny computer into an ammeter or an ohmmeter?