The role of interest groups in American politics is to influence public policy, especially during times when there is no election going on. These groups are a vehicle to keep the conversation going about issues they care deeply about, or even start new conversations. The NAACP is an example of an interest group.
An interest group is not a of fringe group operating on the outskirts of the United States political system, but rather a viable, accepted form of public representation that may be courted by candidates and political parties. Public interest groups support causes that they believe benefit everyone. Animal rights organizations like Mercy for Animals are a type of interest group; they stand for the elimination of animal cruelty.
Greenpeace is a well-known environmental interest group. It has had victories in pressuring lawmakers, including the passing of the Billfish Conservation Act, which stopped the U.S. from importing billfish after previously being the biggest importer; President Barack Obama signed it into law in 2012.
Special interest groups essentially have their own interests at heart. They represent subsets of communities within industries or corporations. Lawyers have them, health professionals have them, oil and gas companies have them and food and beverage companies have them, to name a few examples.