Explain what motivated England to establish American colonies.

The main impetus for English colonization of the New World was economic. Unlike Spanish or French colonial ventures, English colonization was driven by the private sector—by merchants and businessmen who saw the Americas as a boundless source of riches.
To be sure, these colonists had to gain official permission from the English authorities before embarking on their missions, but successive English kings were only too happy to grant royal charters, which they believed would make them players on the international stage. For centuries, the English had been reluctant to become embroiled in Europe's internal squabbles. But at the same time, England aspired to great power status. Establishing colonies in the New World was seen as a way of achieving this goal without going to war with other European powers.
In addition to the enormous commercial benefits that the English saw in the Americas, they also looked upon the New World as giving them an opportunity to settle longstanding religious issues. For orthodox Anglicans, colonization became a useful way of getting rid of dissenting troublemakers. As for the dissenters themselves, the New World gave them a chance to start over, to establish a godly kingdom on earth free from state persecution and repression.

There were a number of motivations for English colonization of the Americas. One of the earliest motivators was competition with Spain. Spain had been making significant inroads into the New World since the beginning of the sixteenth century. After the defeat of the Spanish Armada in 1588, the English felt that the time was right to enter the colonization game. Spain had been growing rich, profiting enormously off its colonies. Now that England had naval supremacy, many English felt that they should be taking advantage of the resources of the Americas too. It was now a good time for England to establish new colonies before the Spanish could regroup and make further inroads into the Caribbean and North America.
Another major prompt for colonization of the Americas was an attempt to address a major economic downturn that was plaguing England. At the start of the seventeenth century, the wool market had collapsed. The wool industry had been one of the major employers of the English rural lower classes. Without this source of income, many found themselves faced with poverty. To solve this crisis, Parliament started to encourage more Englishmen to head to the colonies under the auspices of joint-stock companies in order to bolster the home economy.
A third motivation was freedom of religious expression. Groups such as the Pilgrims and Puritans were chafing under the government-sanctioned practices of the Church of England. They wanted to reform the practices of the church, which they felt were too worldly. However, since the church and the state were one and the same, this put them at great risk. By heading off to the New World—namely the New England colonies—these groups were able to put enough distance between themselves and England to practice their religion as they wished.

England was motivated to establish the American colonies for complex reasons. The sixteenth and seventeenth centuries marked economic changes and the sudden increase in demand for woolen cloth. With the dawn of the Enclosure Acts, landowners could suddenly fence off their farms; this resulted in both an increase in the product of wool to be sold throughout Europe and the sudden uprooting of smaller farmers who had rented plots of land from larger farmers.
Faced with sudden poverty, these migrating farmers hopefully saw the New World as a place for possible re-establishment, while English leaders saw the potential colonization of the Americas as a way to resolve the displacement of these individuals and the poor.
Additionally, England believed that settling the colonies could prove to be profitable, desiring to take advantage the seemingly limitless and untouched natural resources that would be available there. These raw materials could be sent directly back to England so that the country would no longer have to purchase them from other countries. The colonies could then themselves act as a market for England's manufactured goods. 
Thus, out of these political and economic interests, the Virginia Company was granted its first chapter by King James I, giving permission for the joint-stock company to establish their first colonies in Virginia.