The Space Race was a long-lasting competition between the United States and the Soviet Union between the years of 1957 to 1975. It began with the delivery of the first artificial satellite, Sputnik, into orbit in October 1957. When exactly it ended is hard to pin down, but the first joint US-USSR mission in July 1975 is often cited. An alternative starting date is the launch of the first intercontinental ballistic missile, R-7 Semyorka, just six weeks before the launch of Sputnik.
Many historians consider the Space Race to be an extension of the Cold War. The USSR and US were competing to outdo each other in the mediagenic field of space exploration, in an effort to prove that their system of political organization (Communism vs. Capitalism) was superior. Although the Soviet Union had a very strong start, launching the first satellite and the first human into space, the US eventually triumphed in the long run, landing the first man on the Moon. By the mid-70s, the Soviet Union was entering an economic downturn that would signal its eventual collapse, and this forced it to cut way back on funding its space program.
The competition was intimately connected to military superiority as well as general technological superiority. The weapon of choice if the Cold War turned hot would be intercontinental ballistic missiles, suborbital launch units. Opposing countries would have an interest in disabling the spy satellites of the other side, but most of all, both countries wanted to show the world their general superiority.
When Sputnik launched on 4 October 1957, it put the Americans into a state of panic. It quickly became easy to get funding for space-related projects from the US government, and the National Aeronautics and Space Administration (NASA) was founded. In 1961, US President John Kennedy said that the United States should put a man on the Moon by the end of the decade. This was achieved in 1969, largely putting an end to the Space Race.