The Red Scare refers to the wave of hysteria that swept across the United States and concerned the threat of Soviet collaborators within the country.
To describe where it came from and how it grew so quickly, the first thing you need to recognize is that there were legitimate concerns. This was the Cold War, and furthermore, the Soviet Union did employ espionage against the United States and its allies. To give just one example, consider physicist Klaus Fuchs, who gave the USSR information relating to the atomic bomb (and later implicated the Rosenbergs). Even before McCarthy entered the picture and the Red Scare really began to escalate, there were still serious undercurrents of fear and anxiety already present within the country.
The critical figure within the Red Scare was Senator Joseph McCarthy, who made fearmongering into a political weapon. Between 1950 and 1954, he built his political profile around this issue and made a series of denunciations and accusations concerning alleged communist infiltration. These political actions inflamed popular opinion across the country, resulting in an atmosphere of suspicion and paranoia in which anyone could be a potential communist sympathizer.
The consequences were corrosive. Again, this was hysteria, so the mere suspicion of guilt was usually decisive in and of itself, and it claimed thousands of victims in the American public. People were blacklisted, lost their jobs, and had their reputations destroyed.