CODEC is short for 'Compressor-Decompressor', 'Coder-Decoder', or 'Compression/Decompression algorithm'. A codec is technology used for compressing and decompressing data. Codecs can be implemented in software, hardware, or a combination of both. Some popular codecs for computer video include MPEG, H.264, Indeo, and Cinepak.
To play back an encoded file you will need to have the appropriate Codec installed. This is a usually the reason why you will be unable to play back a certain file.