A voltage divider
Two resistors in series across a supply split its voltage. Height here shows voltage: the top wire is at 9 V, the bottom at 0 V, and the point between the resistors sits in between.
The supply
The 9 V battery lifts the top wire 9 V above ground and drives current clockwise around the loop (yellow particles).
One current through both
R1 and R2 are in series, so the same current flows through each: I = 9 V / (2 kΩ + 1 kΩ) = 3 mA.
Voltage splits by resistance
Each resistor drops I × R. R1 (2 kΩ) drops 6 V and R2 (1 kΩ) drops 3 V: the bigger resistor takes the bigger share, which is why R1 spans more height.
Taking the output
The midpoint is tapped as the output. Vout = Vin × R2/(R1+R2) = 9 × 1/3 = 3 V. Change the ratio of the resistors and you change Vout.
Measuring without disturbing
A voltmeter draws almost no current, so it reads 3 V. A load that draws real current acts like a resistor in parallel with R2 and pulls Vout down, so dividers suit light loads.