This 555 timer based circuit is a kind of voltmeter, also an analog to digital converter, that converts the analog input voltage to digital output pulses. The output pulse width is proportional to the difference between the analog input voltage and the voltage across the 4.7 uF capacitor namely 2.5V. It can measure from +5V to +18V
The accuracy is high in the range of 6V to 18V. The readings are about the same with the 10 bit ADC readings. The accuracy depends on only the +5V supply voltage and the microcontroller’s clock frequency. The author uses a Basic Stamp in his project.
You can also measure down to 4V but the accuracy reduces dramatically.
The frequency of the 555 timer is not linear but this situation does not affect the result since the voltage reading depends on only the pulse width, not the frequency.
A sample voltage calculation method is also given in the project page.