how do we measure capacitance ?

I have used AD7746 converter and connected it to arduino. So, measuring probes are sensing and give me expected result. However, i didn't understand the background of the process. We are not directly measuring capacitance with AD7746 converter. what does converter sense or receive at first?

Excitation signal is loading probes and then we receive voltage drops and convert it to digital value. However, what is exactly sensed and calculated? Impedance? How does it work while we are using dc power of arduino?

The theory of operation of the AD7746 "24-Bit Capacitance-to-Digital Converter with Temperature Sensor" is described in the device data sheet.

The sensor relates the amount of charge transferred to the capacitor voltage according to the fundamental equation defining capacitance: Q = CV.

Like all sigma-delta converters it balances charge.

In a sigma-delta ADC packets of charge are added to or removed from a capacitor to balance an incoming
current. Counting the charge packets over time measures the current.

The input circuit just has to produce a charge or current proportional to what you want to measure, the AD7746 uses a voltage excitation signal to the other end of the capacitor under test, and presumably measures total charge to charge and discharge the cap.