36, 42 or 48 bits
This factor is less important today, the price of technology has come down. 30 bits wasn't enough, but we have reached 36 bit technology, and most scanners are 42 or 48 bits now. Color scanners have three internal Red/Green/Blue channels (RGB) of 12, 14, or 16 bits each. The three RGB channels together total 36, 42, or 48 bits for color images. Each binary bit is a power of two that doubles the maximum numerical value that can be stored - which is up to 4096 unique values in 12 bits, 16384 values in 14 bits, or up to 65536 values in 16 bits. More values allow smaller interval steps in the data, and more bits also hold the larger numbers needed to represent greater range of more steps. However, more bits in the container do not ensure or predict or even imply that greater data is actually available from the CCD.
Scanners typically output 24 bit color images, because we need 24 bits (256 unique values in each 8-bit RGB channel) for external purposes like video screens and printers. But more bits internally within the scanner are a big plus that allows tonal and gamma manipulation with less loss of the intermediate tones. Performing this tonal adjustment on 36 bit data and then outputting 24 bits gives better results than manipulating the 24 bit data directly. Some scanners can output their full 36 to 48 bits for external image adjustment into programs that can accept it.
Photo prints and printed paper documents do not have nearly as much dynamic range requirement as film does. So dynamic range is mainly only a concern for scanning film, because only film has the greater density range.
A/D converter chips (analog to digital) are used to transform the analog voltage output from the CCD sensors into the binary values we see. The price of A/D chips has dropped greatly, allowing even inexpensive scanners to use 48 bits now, but don't assume these inexpensive scanners perform better than a more expensive 36 bit model just because they are 48 bits. 36 bits is good, but 48 bits is frankly less important. Even top of the line CCDs don't have noise levels that low. Mostly it just means 16 bit A/D chips are inexpensive now.
A large wallet is needed to carry a lot of cash, but having a large wallet does not mean it is full of cash. There is a big difference in these concepts. 36 bits are needed to hold the large numbers characteristic of large dynamic range, but it does not ensure the scanner CCD can produce those numbers in any meaningful way. Price more nearly indicates good dynamic range, and bit count is necessary to hold it, if it might be present. Shoot for 36 bits over 30 bits, but see next paragraph.
This is very important for scanning film, and it is largely a question of price. Dynamic range is not much concern for flatbeds scanning prints, the scanners today can handle the range of any photo print. Reflective photo prints don't have much dynamic range to be concerned about. But film, especially slides, needs lots and lots of this. Honest dynamic range is extremely important for scanning film, especially slides.
However, you should know that the numerical rating is unfortunately abused (more). The real problem is that there are no standards how this number can be advertised, and excessive marketing hype has caused the number to lose all significance. The advertised number is greatly exaggerated and meaningless. Scanner price is a better indicator of quality than the advertised numerical rating.
Inexpensive scanner specifications don't mention dynamic range for good reason. It is sufficient for prints and documents, but it would not be impressive for film. Good dynamic range requires careful scanner construction with high-quality low-noise electronics, which is not inexpensive.
Results are the only real rating, the ability to capture detail in the dark areas of slides, and the lack of electronic noise in those dark areas. Don't expect a $150 scanner to compete with a $1500 scanner. However, if scanning photo prints, you don't much care about dynamic range. But if scanning film, particularly slides, you will have fantasies day and night about dynamic range, you can't get enough of it. And dynamic range costs real money. Today's better scanners are much improved however, they do a very decent job.