Government does not create interest groups, which are usually called special interest groups. Special interest groups are created by groups of people who have special interests in common, interests they want the government to do something about. They do this by calling the attention of the government and the attention of the people to what their needs are, in the hopes of bringing pressure on government officials who will then act on behalf of their cause. In the United States, this is perfectly legal, since the First Amendment of the Constitution protects the right to free speech, to free assembly, to free association, as well as the right to petition the government about grievances.
There are countless special interest groups in the United States. Three examples are the American Association for Retired People (AARP), the National Rifle Association (NRA), and local parent-teacher associations (PTAs.) AARP protects the interests of senior citizens by lobbying the government on issues such as Social Security and Medicare, to protect these programs on behalf of its constituency. The NRA lobbies the government to protect its members' rights to own and bear guns. Local PTAs lobby school districts and communities to ensure a good education for the local students.
The political significance of these groups is that although we elect officials to create policies and enact laws on behalf of all, special interest groups spend huge amounts of money and energy to influence these officials to provide for their own special interests, and this is not necessarily of benefit to all those whom the officials represent. Individuals who also have needs tend to be unheard and overlooked, allowing those with the loudest voices and the largest budgets to dictate policy on behalf of only a few. In a world with limited resources, there are winners and losers, and the political strength of special interest groups can sometimes dominate in an unhealthy way.
On the other hand, in a country in which we do have the right to speak, assemble, associate, and petition the government, it is not possible to make special interest groups go away. If we were to do so, we would be sacrificing precious, hard-won rights we would be sorry to lose.
If there were a way to magically balance our rights and the those of special interest groups in a way that allowed them a voice that did not drown out the rest of us, I would very much like to know what that would look like.