As can be seen in the adjunct Timeline, there were many "events" in Dutch history that played some part (minor or major) in the establishment of Carolina. As one of the "players" on the North American colonization stage in the 1600s, The Netherlands - informally known as the Dutch - came to the New World with the express purpose of settling it with their people. The Dutch were not looking for quick riches of gold, silver, or even furs. They simply wanted new lands and a new start.
Prior to 1477, The Netherlands were under Burgundian rule. That year, the Burgundian lineage ended with the death of Charles the Bold, but his daughter had married into the much larger Hapsburg dynasty, which immediately took over where the Burgundians left off. Although quite powerful, the Hapsburgs were not invincible. In 1568, the Spanish arrived - and proceeded to take over The Netherlands by force - they simply wanted a tactical location closer to their major adversaries, England and France.
Europe did not take this act lightly. Immediately, the Holy Roman Empire sided with the Hapsburgs and tried to remove the Spanish. For years they were not very successful, and then the Holy Roman Empire joined with the Spanish royalty - thanks to convenient marriages - and the Holy Roman Empire backed off. Then came the English and the French to take up the sword. It took another thirty (30) years to force the Spanish out of The Netherlands, but in 1648 the Treaty of Westphalia brought about independence for The Netherlands, even though the Dutch had considered themselves independent as early as 1579 - merely an act of defiance, for the most part.
During all of this, the Dutch, however, did manage to find the New World and immediately began settling it. With Spain trying to control their daily lives, it's no wonder that the Dutch would want to find new lands.
From 1609 to 1614, Henry Hudson, under contract with the Dutch West Indies Company, explored the coast of what is now called New York, New Jersey, Delaware, and Pennsylvania. Of course, Hudson Bay is named after him.
The first Dutch settlement was Fort Nassau in 1615 - near present-day Albany, New York. It was abandoned three years later. In 1626, Peter Minuit settled New Amsterdam - the famous story of him purchasing Manhattan from the Indians is true - he got it for trinkets. Of course, it may not have been theirs to sell, but who cares? The Dutch settled Kingston next.
Side story - Peter Minuit later went to the Swedish government and convinced them to bring settlers to the New World - he had been "dismissed" by the Dutch, so he sought other avenues. The Swedes began settling along the eastern seaboard in 1638, in direct competition with the Dutch. Take that!
As mentioned above, The Netherlands obtained their independence from Spain in 1648. Soon, they were embroiled in their own wars with England - the first Anglo-Dutch War was from 1652 to 1654.
In 1655, the Dutch seized all of Sweden's assets in the New World, and the Swedes could do nothing about it.
Nine years later, in 1664, the English seized all of the Dutch assets along the eastern seaboard, sparking the second Anglo-Dutch War (1655-1657). But, the Dutch never regained control of their New World colonies. The third Anglo-Dutch War (1672-1674) settled nothing, and the Dutch finally gave up on colonization in North America, although they continued in the Carribean.
The Netherlands were involved in several other significant wars of the late 1600s, but these had no influence on the North American colonies.
So, what was the Dutch "influence" on Carolina? Much more than you might expect. Thanks to the Spanish invading The Netherlands in 1568, this act brought about a war that tied up Spanish assets for eighty (80) years. It brought it the English and the French - on the same side for a change. And, it tied up most of all other important European nation-states.
Combined with all the other wars that involved the English, the French, and the Spanish, this kept the eastern seaboard English instead of French or Spanish. So, we all have to thank the Dutch for their sacrifice. I'm sure they appreciate our thanks, huh?
On a final note, in 1671 - one year after the new Charles Town was founded - many Dutch came to Carolina from New York and Holland, the first of many Dutch settlers to come to Carolina in succeeding years. By the first US Census of 1790, the Dutch population of both North Carolina and South Carolina was less than 1/2 of one percent - so, one can certainly say that the "direct" Dutch influence on Carolina was fairly insignificant. But, they made up for it by keeping the Spanish out for eighty (80) years. Again, thanks!