Wheels have been historically important because they have allowed transportation and trade to happen more easily than they otherwise would. They have also made warfare more mobile. These two factors have contributed to the constant expansion of civilizations to the point where we now have a very interconnected world system.
The wheel gave people greater mobility. It allowed people to engage in peaceful trade more easily than they once did. It allowed goods to be pulled in carts. Eventually, it allowed the invention of railroad cars and automobiles. These inventions gave trade a tremendous boost.
The wheel also made war more mobile. This started with the invention of the chariot. Later, it allowed military supplies to be carried by trains and trucks and it allowed for such things as tanks.
These factors increased the amount of contact between areas and regions. They helped to create a situation in which both war and trade tended to help do away with small countries and create bigger countries. This helped bring about the situation we now have with large countries that are in close contact due to trade.
The wheel was an extremely important technological development, almost as significant as the ability to control and use fire. Civilizations that made use of the wheel had a greater ability to produce food, manufacture goods, and transport goods and people than those that did not. Because making wheels required metal tools, the wheel added a sort of multiplier effect to the unequal development in various civilizations in different geological areas.
Perhaps the first use of the wheel was for making pottery. The potter's wheel allows faster manufacture of pottery of higher quality. Pottery itself was an important part of early civilization, providing insect- and vermin-proof storage for food, liquids, and other important goods and containers usable for cooking. It was also a medium of artistic expression and useful in trade (one cannot trade wine or olive oil, for example, without secure containers).
Next, water wheels were one of the earliest sources of power other than human muscles. They were a way to put the power of streams flowing down hill to various uses such as creating watermills, used in grinding grain, mining, and other manufacturing processes.
Finally, the wheel was useful as a means of transportation both for civilian and military purposes. Existence of the wheel led to development of road networks and postal and courier services which were economically and militarily advantageous.