From Gretchen Siegchrist,
Your Guide to Desktop Video.
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Definition:

Codec is a short name for coder-decoder, the software that takes a raw data file and turns it into a compressed file. Because compressed files only contain some of the data found in the original file, the codec is the necessary “translator” that decides what data makes it in to the compressed version and what data gets discarded.

Different codecs translate in different ways, so a video file compressed using the Intel Indeo codec will be different from a file compressed using the Cinepak codec, for example. Sometimes the difference is noticeable, sometimes not, but it’s good to be aware of what codecs are best for what you’re trying to do in order to maintain the best ratio of file size to quality.