Explain how human beings interact with the Hudson River in "Our River." What kinds of activities do inhabitants enjoy on the river? What resources does the river supply? How do nature and culture interact?

I believe you are referring to the writing “Riverby” written in 1894 by John Burroughs, which is part of his twenty-three volume Complete Writings. John Burroughs was a literary naturalist (that is, he wrote about nature rather than conducted scientific studies) who was born on a farm in the Catskills in 1837. He was always interested in nature, and when he met Walt Whitman in Washington, DC, in 1864, Whitman encouraged him in the writing of nature essays. In 1873, Burroughs bought a farm in the Hudson River town of Esopus and entertained Whitman and such conservation giants of the time as Teddy Roosevelt and John Muir. He continued his writing up until the time of his death in 1921.
The Hudson River has had a major impact on the cultures of various groups who have interacted with it over many centuries. The Native Americans who lived along its shores called it Muhheakantuck, meaning “river that flows two ways” as it is tidal and saline as far as Poughkeepsie. The Native Americans relied on it for transportation, a variety of fish, oysters (important for the making of wampum), and the meat and pelts of wild game that lived along the shore, as well as the turkeys and nuts found there. They built villages and planted squash, beans, corn, pumpkins, and tobacco.
Henry Hudson explored the river when looking for the Northwest Passage to the Orient and claimed it for the Netherlands. At that time, they called it the North River. The Dutch, who were impressed by the beauty of the area, were more interested in trade than settlement and built trading posts along the river to trade for beaver pelts, which were in high demand for hats in Europe at that time.
Since the culture of the Dutch emphasized trade over settlement, it was easy for the British to take control of the area in 1664. They saw it as a strategic location for increasing their dominion in the New World, and built a series of forts between lower Manhattan and Albany. The Native Americans became embroiled then in the European struggles, especially between the English and the French.
The Hudson River continued to be important because of its natural resources and geographic location after the Revolutionary War. As the new nation grew, the Hudson became linked with western expansion via the Erie Canal. In 1807, at one of the large Livingston family estates along the Hudson, the steamship Clermont was developed. Agricultural products were transported, and as the culture shifted in the Industrial Revolution, manufacturing developed, especially in the Albany and Troy area. Railroads developed along its banks. IBM set up huge complexes around Fishkill and Kingston between 1941 and 1996. At the same time, the Hudson was beloved for its beauty in both the nineteenth and twentieth centuries. Wealthy families owned huge estates and raised apples and race horses, employing tenant farmers from the Palatine region of Germany. Hotels for summer guests sprang up, with guests brought by ferries and trains. The Hudson River School of painting was developed.
Along with the growth of industry, the pollution of the river became rampant, and in the late twentieth century, the Environmental Movement became a major cultural influence, led by folksinger and activist Pete Seeger. Nature and culture along the River continue to be deeply intertwined.