A social movement is simply a group of people working to achieve a common goal that is usually focussed on a political or social issue. Social movements arise when an organized collection of people begin to campaign for a change in society in response to what they perceive as being a problem or injustice or unanswered need. Examples of social movements could be the Civil Rights movement of the 1960s, the efforts to legalize same-sex marriage, the Arab Spring demonstrations against governments in northern African nations, and the Occupy Wall Street gatherings that are currently spreading to other cities and nations around the world.
Two other very important examples of social movements, to give you some comparisons and contrasts to the Civil Rights Movement, were the Women's Suffrage movement of the 1800s and early 1900s, and the Temperance movement of the same time periods.
As in the Civil Rights Movement foir African-Americans, the Women's Suffrage movement sought to address discrimination and sexism where women's political rights were concerned. Notice, when we talk about movements, they cover an extended period of time, as opposed to a protest or other isolated incident.
The Temperance movement was religiously and morally based, but had strong ties to the Women's Suffrage movement. Often times we can find large scale social movements that seek not only equality between humans, but a moral society with a strong family unit.
A social movement is an effort by a large number of people to create some sort of change in a society. A social movement is typically undertaken by some group that is not able to achieve its goals through more conventional political means.
Perhaps the most famous social movement in recent US history was the Civil Rights Movement of the 1950s and 1960s. In that social movement, there were a large number of people (mostly African American) who wanted to change their society to give blacks equal rights. They were not able to accomplish this through regular electoral politics and so they turned to protests and other forms of action that are more common to social movements.
So, as the link below says, a social movement is
An organized effort by a significant number of people to change (or resist change in) some major aspect or aspects of society.