The "missile gap" was the (unwarranted) fear that the Soviet Union would have the capability of building and deploying Intercontinental Ballistic Missiles (ICBMs) before the US had such a capability. During that time, there would be a gap between US and Soviet power.
This fear came about largely because of the launch of Sputnik, the first artificial satellite to be put into orbit around the Earth, in 1957. The fact that the Soviets could launch a rocket that would put a satellite into orbit made Americans fear that the USSR would soon have ICBMs. Since the US had no such missiles, fears of a missile gap arose.