The VOC had trading posts along the coast of Africa, the southern tip of India and many of the islands that make up Indonesia. The West India Trading Company had territory along the coast of South America and in modern-day New York.
The Dutch established a colony called New Netherland in the northern part of what is now the United States which they mainly used for the fur trade. New Amsterdam (named after Amsterdam, the biggest city in the Netherlands) was the city where most colonists in New Netherland lived.
Unlike the British and Spanish Empires, the Dutch Empire was mostly focused on trade, not on settling in their colonies. The Dutch Empire mainly consisted of small outposts near the coast and along trade routes which quickly fell when attacked by foreigners. The Dutch eventually lost much of its empire to the British. When the British captured the colony, they changed the name of the city from New Amsterdam to New York.
The Dutch Empire helped establish a global trade market, introduced Europeans to many luxuries like spices and tea from the East, enriched their trading partners and pioneered the stock market.
At the same time, it exploited the native people in the lands they conquered and took away their freedoms. The book "Max Havelaar" by the Dutch author Multatuli described the abuses of Dutch imperialism and started an anti-colonial movement in all of Europe.
Today, most of the former Dutch colonies are independent nations. However, the Caribbean islands of Aruba, Curacao and Saint Maarten remain part of the Kingdom of the Netherlands.
