공강 literally means "no/missing classes" - it indicates the time when there is no class (for students on campus). For instance, if you have a one hour class at 9:00 and another at 11:00, your 10 o'clock hour is called 공강: 공 = empty, 강 = 강의(class, lecture). 우리 공강시간에 잠깐 만나는 거 말고 주말에 만나는 거 어때? = What do you say to us meeting on the weekend instead of during the free time between classes? 응, 그 인간들 때문에 공강시간에 약속 잡았는데, 그럴 이유가 없잖아 = Yeah, I only set the meeting for the free time on campus because of those guys, but there' really no reason to do that.