In the context of trade and immigration, borders are often discussed as a means of excluding foreign workers and foreign goods. In one way of thinking, borders provide an opportunity for states to exclude private actors such as workers, merchants, and entrepreneurs. On the other hand, borders can also serve a far more endearing function, and this is found in the fact that borders represent the limits of a state's power. That is, while borders may exclude goods and people, a state's borders also often exclude other states.
For example, East Germany's border with West Germany represented the limits of the East German police state, beyond which the power of the Stasi to kidnap, torture, and imprison peaceful people was far more limited than it was within its native jurisdiction. The West German border acted to contain the East German state.
Similarly, the borders of Saudi Arabia delineate a limit to the Saudi regime's ability to behead people for sorcery or for making critical remarks about the blood-soaked dictators known as the House of Saud.
Even within a single nation-state, borders can illustrate the benefits of decentralization, as in the case of the Colorado-Nebraska border. On one side of the border (i.e., Nebraska) state police will arrest you and imprison you for possessing marijuana. They may kill you if you resist. On the other side of the border, the state's constitution prohibits police from prosecuting marijuana users. The Colorado border contains Nebraska's war on drugs.