FIP is similar to ERA, but it focuses solely on the events a pitcher has the most control over -- strikeouts, unintentional walks, hit-by-pitches and home runs. It entirely removes results on balls hit into the field of play.
For example: If a pitcher has surrendered a high average on balls in play, his FIP will likely be lower than his ERA. Balls in play are not part of the FIP equation because a pitcher is believed to have limited control over their outcome.
Where the "FIP constant" puts FIP onto the same scale as the entire league's ERA: ((HR x 13) + (3 x (BB + HBP)) - (2 x K)) / IP + FIP constant.
Why it's useful
Because FIP is limited to the events a pitcher has the most control over, it's arguably a better tool than ERA for evaluating a pitcher's effectiveness. It's also useful for predicting a pitcher's future results, because a pitcher has little control over what happens once the ball is put in play behind him.
A pitcher with a low FIP but a high ERA has most likely seen a string of bad luck on balls in play. He could be a buy-low candidate, assuming he eventually gets league-average results on balls in play.