Optical density, also known as Dynamic Range, is the scanner's ability to "see" all tones available. The total tonal measurement is on a scale of 0.0 (white) to 4.0 (black). The question is, how much of this 4.0 range can a scanner distinguish?
This is a spec that many scanner manufacturers shy away from, yet it is one of the most important to consider. It is also one of the most expensive to improve upon.
Many consumer-grade scanners have a somewhat limited Optical Density of approximately 2.5.
High end drum scanners (typically limited to commercial ownership and use due to their high cost) have an Optical Density upwards of 3.8 to 4.0 which represents about 95% to 100% of the original source's tonal range.
Another way to think of Optical Density is contrast. A scanner with limited Optical Density ability yields a higher-contrast image that has lost highlight and shadow detail. Conversely, a scanner with a high Optical Density ability yields a full range of tonal detail from shadow to highlight areas. You can always effectively increase contrast (discard some tonal detail) in an image scanned with a high quality scanner, but it is not as effective to attempt to reduce the contrast (increase the tonal detail) of a low quality scan since the detail was never there to begin with.
In summary, Optical Density represents how much of the original's (scanned source) total tonal information is represented by the scanner.