It is not the same as a gfx card benchmark, it is a scientific measurement of the electro-optical properties of the sensor ignoring the affects of lens optics and normalizing for a common print/display size.
They basically measure the signal to noise ratio under various conditions and limits. The SNR is a key indicator to explain how much true data a sensor is collecting rather than noise. The nitty-gritty numbers are summarized as 3 numbers relating to photography, bit depth, noise performance and max Dynamic range. The Dynamic range has a clear application to your every day photography. E.g. if you are taking a landscape photos and the sky gets clipped to pure white you might use a 2 stop ND grad to bring down the exposure of the sky. If one camera has a 2 stop dynamic range advantage over another camera, then you could get away without the 2 stop ND-grad and reduce the exposure appropriately software. A few caveats exist, but that clearly shows a direct application to your photography.
the same is true of the high ISO noise. Basically they have decided on some thresholds that must be reached to say that a photograph is of sufficient quality, basically not too noisy and enough dynamic range. The ISO sensitivity of the camera is increased until these thresholds are not met, this is then the max ISO that the camera can be used at to still maintain the sufficient image quality. The ISo rating is not the actual ISO setting on the camera which are all incorrect by some amount, but the true International Standards Organization (ISO) definition of the sensor gain needed to achieve the correct exposure of a grey card that has properly calibrated lighting. E.g., you cannot compared ISO 1600 on 1 camera with ISO 1600 on another camera because the manufactures may apply different amounts of amplification that is correct. DXOmark removes these differences so one can accurately compare noise performance.
One DXomark don't do is look at the pattern of the noise and difference between chrominance and luminance noise. Typically Nikon sensor have produced higher amounts of lumiannce noise (black and white) and lower amount of colour noise due to their noise filtering, which helps preserve details but still looks nice. Canon typically reduced luminance noise more strongly and left some chrominance noise, so the Canon noise was more objectionable even if it gave lower noise values.
The differences are less strong now between nikon and Canon but there are other issues. E.g., the 5DMkII has very severe banding in the shadows, DXOmark does indeed give a lower Dynamic range score due to this banding (see the score), but the banding is much more visually obtrusive than the raw numbers would dictate because repeating structured patterns are far worse visually than true random noise. In fact true random noise is more commonly refereed to as grain, and some sensors when they produce noise often produce "film-like grain" where although the noise is higher, the noise is uniform and mostly black and white and is just less ugly than large colour blotches.
