Codec is shorthand for "Encoder/Decoder". A codec allows to convert data into a different representation and decode it again. Codecs are mostly used in signal transmission, e.g. for audio/video playback or streaming.
In practice, this distinction isn't made, and therefore "codec" will mostly be used synonymously with "encoder". For a list of popular codecs and the difference to actual file formats, see: What is a Codec (e.g. DivX?), and how does it differ from a File Format (e.g. MPG)?
Some popular codecs on Super User include: