There are many things that could be seen as “main ideas” about the space race and the moon landing. Let us look at a few of them.
First, the space race began in earnest in 1957. The Soviets really started the space race in that year when they managed to launch Sputnik, the first artificial satellite ever put into orbit. After the Soviets launched Sputnik, the US desperately tried to get ahead in this race.
Second, the race was caused partly by Cold War fears of Soviet weapons. Rockets that can carry payloads into space can also be used as nuclear missiles. Because of this, the space race really mattered for national security. If the Soviets had missiles and the US had none, the US would have been vulnerable.
Third, the space race was caused partly by a desire to show that our system was better than that of the Soviets. Outside of its military implications, we cared about the space race because we wanted to be better than the Soviets in every possible way. If we won the space race, it would make our capitalist/democratic system look better than the Soviets’ communist system.
Thus, the space race was something that began in 1957 and essentially ended with the moon landing in 1969. It was caused mostly by Cold War competition between the US and the USSR.