By the early 18th century, the British had outstripped both French and the Spanish in the New World by becoming the most populous prosperous and powerful. explain how this happened
By the early eighteenth-century, Spain had been colonizing and exploring South America on a grand scale for over a century, primarily to extract wealth and send it back to Spain. Although there were Spanish colonies in South America, they tended at first to be made up of Spanish administrators and religious elements (for the most part, Jesuits). Because the main goal was to extract wealth from the land, the Spanish imported hundreds of thousands of Africans for slave labor. Native Americans either became part of the labor pool or were exterminated. Although eventually there were thousands of Spanish civilians in Mexico and South America, intent on living there, their interests focused on South America rather than North America, and they simply did not try to colonize areas above Mexico on a large scale. The Spanish did establish some colonies in Florida, for example, St. Augustine, but not on the scale the English pursued.
The French concentrated their colonial efforts in the 17th and 18th centuries on Canada, and by the early 18th century, the French had a sustainable group of colonists in eastern Canada, particularly in Quebec and Montreal. Although they also sent expeditions into the Ohio Valley, these were mostly military in nature and allowed the French to claim the territory. There was not, however, a large influx of French colonists into these areas. Instead, small groups of French used the territory to hunt and trap beaver on a huge scale for economic purposes. The French tended to co-exist with Native Americans rather than exterminate them, often inter-marrying with them, and so French and Indian relations were often peaceful.
English colonial policy, on the other hand, encouraged thousands of English immigrants to populate areas of what we know call New England and south to Virginia. Rather than sending only military troops, England sent tens of thousands of civilians whose goal was to make a new life in the colonies. When they arrived, their primary goal was not to extract wealth and ship it back to England but to create a "new" England. One of the negative results of this was the ultimate displacement (and extermination) of Native Americans who would not peaceably give up their land to the English (I'm simplifying this, but not by much). A positive aspect of the English influx was the creation of permanent settlements and land improvement for a sustained presence in North America.
Before the early eighteenth century, England was the weakest of the three European nations vying for control over North America; by 1750, England would possess most of the continent. While Spain and France did send colonists to the New World, England sent more of them. The English colonists were permanent—in Plymouth they were religious dissenters, and in Georgia they were debtors who would not be welcomed back to England. Spanish and French colonists, on the other hand, were largely traders and missionaries who did not want to start families in the New World. England developed the New World for its own ends, and in times of war with the other two powers, it could count on its loyal colonists to drive out the other powers.
Another factor here is that England would develop the strongest navy the world had ever seen. Its navy, privateers, and merchant fleets were more numerous than those of both Spain and France. Not only did England possess the New World, it could also send supplies and protection to these colonists. Not only did the navy allow England to possess the New World, it also opened up more areas around the world for colonization.