Pixel Density is a calculation of the number of pixels on a sensor, divided by the imaging area of that sensor. It can be used to understand how closely packed a sensor is and helps when comparing two cameras with different sensor sizes or numbers of photosites (pixels). Because the light collecting area and efficiency of each photosite will vary between technologies and manufacturers, pixel density should not be used as a predictor for image quality but instead as a parameter to help understand the sensor.
Diagram comparing some common sensor sizes
The APS-C sensors used in most modern DSLRs have an area of approximately 3.5 cm², while the 1/1.7" and 1/2.3" sensors commonly used in compact cameras have areas of 0.43 and 0.29 cm², respectively.
To get some idea of what this means, here is a diagram representing a pixel density of 28 MP/cm² (the pixel density of the Canon G9). As you can see, this density equates to 12 MP on the G9's 1/1.7" sensor but would be 91 MP if applied to a sensor as large as the one in a Canon 450D.
Conversely, if we look at the Canon 450D's pixel density of 3.7 MP, we can see that it gives 12 MP on a Canon APS-C sensor but would give just 1.6 MP on a 1/1.7" sensor like the one in the G9.
The calculation is based on the number of pixels produced at the camera's native resolution (Effective pixels), so both for conventional Bayer sensors and Foveon type, one photosite is considered equal to one pixel in the final image. For Fujifilm's Super CCD SR technology, each photosite contains one 's' and one 'r' photodiode but contribute only one pixel to the final image, so are classed as a single pixel.