FEC can mean two things in Internet terms, depending on the context.
1) FEC is an acronym for Forward Error Control. Essentially, using some very cool mathmatics, the addition of some extra CRC-like bytes to the data packet can allow you to correct a limited amount of bit errors. It is particularily useful for error-prone links such as DSL or satellite communications.
2) FEC, in MLPS terms, stands for Forwarding Equivalency Class, used for routing choices.