There is an intrinsic quality of the camera sensor and analog processing called "noise figure". Analog circuits with a higher noise figure means that the random fluctuations in the noise current has a wider spread (variance, in mathematical terms) than circuits with lower noise figures, given that they are at the same temperature.
Nikon uses a noise reduction process that is worth understanding. (I suppose other makers have something similar.) In this NR process, a dark image is recorded from the sensor, with the shutter closed. This is done immediately after the real picture is taken, so it is done under the same conditions (same temperature) as the original picture. It then subtracts the sensor noise from your real photo. (You must choose to enable this NR process).
What does this mean?
First, you should understand that what the sensor is recording is an accumulation of the effects of photonic and electrical current over the duration of the exposure. The longer the exposure is, the longer this accumulation takes, and the sensor noise from dark current builds up. If the shutter is open, this accumulation of sensor noise also has an accumulation from the image intensity added to it. The accumulation results in a measurable electric charge at each pixel of the sensor. The amount of charge is proportional to the photonic power plus the noise power that it is sensing.
This sensor noise can be different for every pixel in the sensor. This is because there may be minute differences in noise figure for each pixel (even though they are manufactured on the same wafer, or chip). So some pixels will have more noise than others, even though they are at the same temperature.
What is an exposure, exactly?
In the description above, and exposure is not just the time the shutter is opened. At the same time, the sensor must be operated. At the beginning of an exposure, every pixel must be drained of any electrical charge caused by the previous exposure and any noise since the previous time it was cleared. This is a reset to zero, so to speak. At the end of the exposure, the electrical charge must be measured. Even when the NR dark image is recorded (and the shutter is closed), this sensor processing has to be done. It the circuitry waits too long to measure the charge at every pixel, then noise current can continue to add to the charge.
The final step in NR
Once you have two "exposures" from the sensor, the dark image is subtracted from the real image. The assumption here is that the noise level measured at each pixel is nearly identical, so subtraction removes much of the noise.
Does it work?
I have never tried NR on my camera, but I have seen professional light painters use it. I would take that as an endorsement.
How do I quantify the noise?
As I explained, the noise can be measured by taking a dark exposure. You should be able to do that without enabling a noise reduction feature - just leave the lens cap on and take a picture.
Measuring and quantifying noise figure is a little complicated, but it's a common part of designing any electrical circuits that are sensitive to noise (like your cell phone receiver, for example). There is plenty of literature on how to quantify noise figure, and I won't go into it here (unless you have a specific question, and then I can try to answer it). I don't imagine this would be easy for a multi-megapixel sensor, but it is doable.
This is a statistical measurement, and your results get better if you make the measurement over a longer time.
What else causes noise?
You might see that noise (or noise figure) apparently isn't identical from one measurement to another. There might be other factors that can account changes. One thing to consider is any penetrating radiation. This can include cosmic rays or maybe the radiation from a luminous dial wrist watch (some of us have these!). Radiation like this is all around us, and the camera sensor can pick it up just like a Geiger counter can. I wouldn't expect this to be much, but I haven't quantified it, so I can't say for sure.