There has in history only ever been one space race. Therefore, the more appropriate question is probably “what was the space race.” The space race was a competition in the 1950s and 1960s between the Soviet Union and the United States. This was a competition in which both countries were trying to be the first to achieve various milestones related to space exploration. The two countries wanted to win the space race for two main reasons.
The space race did not have any official beginning. However, it can be said to have begun in 1955. In that year, both the US and the Soviets announced that they would soon be able to launch artificial satellites into orbit of the Earth. The race then heated up dramatically when the Soviets won the race to the first milestone. This occurred when they launched Sputnik, the first artificial satellite, in October of 1957. The Soviets also reached the next milestone first when they put the first human being into space in 1961. The main part of the race that the US won was the race to put a human being on the moon. The US accomplished this in 1969.
The space race was important for two reasons. First, it had military implications. The country that could build better rockets would have an edge in building nuclear missiles. Second, it had ideological implications. Other countries would notice which country was winning the race and would tend to be attracted to that country’s ideology. Thus, winning the space race was seen to be important both for military and for public relations purposes.
The space race often refers to the time in history when nations, specifically the USA and the Soviet Union, were competing in what was known as the Cold War. The Cold War refers to a time period when the United States and the Soviet Union competed with one another in many different areas - particularly new technology in weaponry (especially nuclear weapons) and eventually in the field of space exploration technology.
In the 1950s, the Soviet Union successfully launched Sputnik, which was the first man-made object to orbit the earth. This was a major accomplishment on behalf of the Soviets and the United States did not deal well with the news. As a result, the USA started what is now known as NASA and also began to pass education legislation that they hoped would result in a brighter and more advanced technological future for the United States.
After the Soviets and the Americans made various advancements in space technology, the ultimate goal became landing on the moon. Ultimately, the Americans made the first moon landing in the 1960s, which brought about an end to what we refer to as the "space race".