You got some good answers on what it is, but what it means is more important. Here's a graph of the Dynamic Range of a Nikon D850 from DxOMark.com. The human eye can capture a difference between light and dark of about 20 stops. That's 2^20 or we can perceive something about 1,000,000 times darker than the brightest object in a scene. Higher end cameras can capture around 14 to 15 stops as base ISO, less than the human visual system, but the graph shows that ability drops very quickly a stop or two above base. At the same time the noise (green to red bar on the right) starts to go up. It's a good idea to understand this curve before bumping up ISO and then wondering why the image looks flat and washed out or the highlights are blown out or the shadows are buried. If you are getting blinkies, one option might be to lower the ISO at the expense of shutter speed and/or aperture. At the same time, the number of bits of color a sensor can capture also goes down with increasing ISO.

Good topic OP

Answers are too complicated...

The dynamic range is simply the exposure latitude you can use before you blow one extreme, highlight or dark. The range is a number between 10/16 at the moment. +-5/+-8. The greater the number the better.

The dynamic range is related to luminosity, not color rendition*.

To exploit the full DR of a camera one needs to use raw. A JPG out of a camera will benefit from the camera native dynamic range but will not offer the potential edit that the raw format does.

There is a relation between the sensor element size (density) but this is not of any interest here.

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* Some will dispute that. A correctly exposed capture colors will not suffer from the lack of dynamic range. The color simply will not have the same shade variations.

Read some interesting explanations provided by some of our Hoggers here. One aspect that I have often wondered about is how all this fabulous dynamic range provided by the best digital cameras is captured in what we can view as a picture on photographic paper, steel plates, or just on computer monitors. And compared to what we used to expect from various photographic films. I used to worry about what kind of capture I could produce with reversal films since most had rather narrow dynamic range. Kodachrome was the widest and Ektachrome was very narrow. Even today, how much of the dynamic range captured in camera is able to be produced on a print coming from an ink jet printer or photographic paper. Or for that matter, how much dynamic range can be shown on an iPad or iPhone screen since that seems to be the most used viewing option used today. I have never seen a discussion along these lines. Maybe some of the professionals here could elaborate on that subject.

There is little point to considering "sensor dynamic range" in isolation. We record images with whole cameras. A camera is a system, and every system I've ever worked with is only as good as its weakest point. In photography, with recent cameras, that weak point is seldom the sensor. It's usually the image processing.

Since part of the photography system can be outside of the camera (computer, monitor, calibrator, software, printers, profiles, etc.), it makes sense to focus on that, too, when you're striving to maximize *apparent* dynamic range.

Silver halide photographic paper reflects about 90% of the light falling on it, under the best of circumstances. Out of an 8-bits per channel image, a range of values somewhere between 12-242 and 18-236 is all we see reflected from most papers. That's around 5 f/stops. But with 12-15 stops of range possibly recorded in raw data, what do we do with the other 7-9 stops?

The answer is found in the various sliders in post-processing software. Detail that is "burned out" or "plugged up" in an out-of-camera JPEG may be there in a raw file of the same image. When that is the case, much of it can be "recovered" (tonally compressed to the point we can see it within the range of brightness that the paper or screen can reflect or transmit). Of course, it is possible to make an awful mess of an otherwise good image, by over-applying adjustments. And unless the monitor is properly capable, calibrated, and profiled, adjusting images at all may well do more harm than good.

So take dynamic range analysis of sensors with a grain of salt. In the final analysis, most PEOPLE don't give a rat's patoot what camera a photographer used, or whether it was film or digital, or whether it was full frame or smaller. They care about the art, or the communications value, or the emotional impact of the image. If it speaks to them in a way that has the photographer's intended effect, who cares?

Most of the spec wars don't amount to anything tangible unless we're making HUGE prints on 8-14 color inkjet printers, on really exotic, archival, museum grade papers. That can be important in the world of landscape photography, or point-of-purchase advertising, or copying artist's renderings from paper or canvas. But for the rest of us making 16x20 and smaller prints, or just viewing our images on screens, it's a fairly moot point.