What was the significance of the greensboro sit-in to the civil rights movement?

The Greensboro sit-ins were a number of non-violent acts of civil disobedience that took place in 1960 in the city of Greensboro, North Carolina, with the intention of challenging the racial segregation in the Southern United States. It was not the first sit-in of the African-American civil rights movement but the one that sparked a slew of sit-ins, with the result that racial segregation was abolished in many catering establishments, including Woolworth's restaurants.  

At the time, it was common in the South for whites and blacks to sit in separate areas of catering establishments and sometimes enter through separate entrances. This was regulated by law.

On February 1, 1960, four freshmen from North Carolina A&T State University (the four from Greensboro) sat at a Woolworth's facility in lunch counter areas reserved for whites only. They ordered coffee but were asked to leave what they refused to do. The police were called in and for a while an officer stood behind them, threatening with his bat. They only left at closing time.

On February 2, they returned with twenty other black students and sat down again. On February 3, the group consisted of more than sixty students, and on February 4, more than 300, now from another university. Because the group became too big, it was decided to go to a Kress branch. By February 6, the group had grown to above 1,400. Meanwhile, white students had also joined the group.

From day one, the sit-ins got media attention, and after a week similar protests started in other cities and states. At the same time, restaurants and shops where segregation took place were boycotted. On July 25, the Woolworth's manager in Greensboro asked three black workers to take a seat at the bar and order a meal. They would (quietly) become the first black customers of a Woolworth's establishment to be served in the white part of the business.