A joke term invented by a couple of music blogs to describe the modern emo metal played by the band Attack Attack!, based on the crablike crouch stance often performed by the guitarists / bassist.
It's not a real genre of music, since the term was coined to describe one band which plays a certain style of a much more well defined genre of music. Pretty sure that every band on the planet that has ever had success plays a personal style of some sort of larger, more well defined movement. Attack Attack! is a contemporary emo band, regardless of what they do with their legs. Calling a band crabcore is like calling Owl City a postalservicecore band.