Opposite of square. Groovy is originally an expression from jazz, meaning musical, playable, as in a groovy record. The groove of the record has beat and soul. Something or someone groovy has beat and soul. The term was adopted by the musically inclined countercultures of beatniks and hippies.
What you say to a teammate or friend when the immediate situation is intense and dangerous and you want to remind them to keep focused and on the job. Historically used by military elite spec op team members when they are tired, ground down, there is imminent danger, and they need to keep going to accomplish the mission.