In more detail
The same current flows through both resistors, I = Vin / (R1 + R2), and each drops a share of the voltage in proportion to its resistance. A potentiometer is an adjustable divider, and a sensor such as a thermistor or light-dependent resistor in place of R2 turns a changing resistance into a changing voltage that a microcontroller can read. Anything connected to the output sits in parallel with R2 and lowers it, so a common rule keeps the load at least ten times R2.
Why it matters
Dividers suit signals, not power: the output sags as soon as a load draws current, and the resistors waste power continuously. To supply a circuit, use a voltage regulator. Choosing resistor values is a trade-off: low values waste current, very high values are easily disturbed by the load and by noise.
Example
9 V, R1 = 10 kΩ, R2 = 5 kΩ: 9 × 5 / 15 = 3.0 V
With a 10 kΩ load on the output: R2 ∥ load = 3.33 kΩ → 9 × 3.33 / 13.33 = 2.25 V
12 V into a 5 V ADC, R1 = 15 kΩ, R2 = 10 kΩ: 12 × 10 / 25 = 4.8 V, drawing 0.48 mA