As noted author and philosopher Ayn Rand pointed out, they compete with one another to seize control of the mechanism of law (government) so as to benefit themselves at the expense of other groups...
They give an organized voice to a group of American people with the same opinions. They help Americans raise their voices loud enough for Congress to hear.
Generally, because they represent a specific segment of the overall population. Not everyone is handicapped, so an interest group representing them would be a "special" interest group because...