Along with codec and data rate, digitally rendered video must also calculate color response to an image, and it's fidelity in doing so is determined largely by its BIT DEPTH.
8 BIT, 10 BIT, 12 BIT
These are the most commonly encountered bit depths for digital video - though higher bit depths are possible.
8 BIT - For each color channel (RGB) there are 8 bits of data storage available. This means there are 256 shades of R, of G, and of B. Therefore, there are 16,777,216 possible colors in an 8-bit video image.
This is probably the one most commonly encountered in consumer/ prosumer video production. DSLRs, high-end prosumer video cameras, etc, all record at 8 bit, internally. The commonly-used AVCHD codec is limited to 8 bits; to record at a higher bit depth, one must use another codec, which means for a DSLR et al, an external recorder is required.
8 bit video is very high quality, and if the playback mechanism (monitor, projector, etc) are also 8 bit in their response, then the playback quality is as good as it will get. If, however, the capacity of the playback system is higher than 8 bits, the artifact most frequently encountered will be color-banding in any area of gentle gradation.
Note the faint diagonal lines separating the shades in the sky. Click on the image to enlarge.
10 BIT - For each color channel (RGB) there are 10 bits of data storage available. This means there are 1024 shades of R, of G, and of B. Therefore, there are 1,073,741,824 possible colors in 10-bit video. The tradeoff is that these files will be significantly larger than 8-bit files, so new investments in storage, file management, and data transfer time will be required.
10-bit video can only be recorded internally by a few high-end cameras using their native codecs or RAW format; otherwise external 10-bit recorders, like the Odyssey 7Q or the Atomos Ninja, will be needed.
It should be noted that when paired with RAW acquisition (as the recording codec), 10-bit video will have increased dynamic range due to the higher number of available shades in the dark and light areas of the image.
If the final playback mechanism is only 8-bit, however, the benefits of 10-bit recording won't be apparent. 10-bit is useful, however, when shooting video that will be digitally composited, as almost all image-generating software will create images with bit depths of 12 bits or higher. When pairing 8-bit video with digitally generated imagery or composites (such as greenscreen), the digitally-generated material must be crushed down to the lower bit depth, and the compositing results will suffer.
12 BIT - For each color channel (RGB) there are 12 bits of data storage available. This means there are 4096 shades of R, of G, and of B. Therefore, there are 68,719,476,736 possible colors in 12-bit video. Like 10-bit video, this creates VERY large files; it provides greater dynamic range response in highlights and shadow areas; and it is primarily for the purpose of working with digital postproduction and processing techniques (when acquired through a RAW recording mechanism).
When digital video is being recorded or transcoded, in addition to the bit depth (8, 10, 12) and data rate, there is also consideration of color precision, which is determined by how many samples of each color channel are taken. Like in digital audio recording, higher sampling rates mean higher levels of precision when rendering the signal as a set of bits (of however many bits you've got). To express the relative sampling of the 3 channels (RGB), color sampling notation is written as three colon-separated numbers, usually 4:4:4, 4:2:2, 4:1:1, or 4:2:0. These sampling schemes take advantage of shortcuts in human color perception that are mathematically recreatable in a computer - namely, that given a full sample of one color channel, and only a partial sample of another, it is possible to calculate ALL the values to a reasonable degree of precision such that they won't be readily perceived by a human eye. The benefits of reducing the sampling rate are large savings in storage and data requirements.
4:2:2 for example, takes a full 4 samples on one channel, and 2 off of the remaining channels, and creates a high-fidelity calculation of all those color values. It is also space-saving. However, it is imperfect in its fidelity.
4:4:4 is the most aggressive sampling rate, taking full samples of all channels. Its color fidelity is the best possible; the files are very big.
This high sampling rate is not possible in internal camera recording except in some very high-end cameras. Typically an external recorder will be needed. While most of its benefits are not perceptible to the human eye, its primary benefit is in working with digitally-generated or -processed imagery in postproduction, such as greenscreen composites, where high digital color fidelity contributes to more accurate composites.
Some further reading on color sampling here:
http://www.sounddevices.com/notes/pix/444-vs-422-color-sampling/