The name means 'attack and smash (or destroy)'. It was originally called Fukyugata Ni (Master Shoshin Nagamine, also developing an appropriate entry-level kata for use in Okinawa, had in the same period created Fukyugata Ichi) but Miyagi changed the name when he developed a second kata (Gekisai Dai Ni) and wanted an appropriate name that allowed him to both distinguish his two kata while at the same time making sure the names reflected the fact that they were related.
The kata is linear in its approach and teaches the concept of forming an aggressive mentality and series of techniques to deal with an attack at longer range (traditionally Goju ryu kata emphasize close quarters combat).
Gekisai Dai Ichi performed by Master Morio Higaonna