In order to answer this question, it's important to understand that Great Britain's presence in India was broken into two eras. At the end of the 17th century, Queen Elizabeth I granted the rights to trade in the East Indies to over 200 British merchants. They formed a company known as the Governor and Company of Merchants of London Trading into the East Indies, later shortened to the East India Company.
In India, the East India Company's role was purely exploitative. These merchants wanted only to increase their wealth. For this reason, they were typically harsh with native populations and, as a result, stirred up a great deal of enmity. Early products that merchants brought back from India to sell in Britain included spices, silk, and cotton. By the mid-18th century, the East India Company had assumed full administrative control over its territories and also levied taxes upon the populace. In one of its most egregious acts, when Chinese tea became more profitable than Indian tea, the British East India Company produced opium in India to sell to the Chinese.
The Indian Rebellion of 1857 caused the British government to take direct control over India as a colony. This era became known as the British Raj. Although Great Britain helped to develop India by creating a railway system, telegraph lines, postal services, and better sanitation and lighting, it also continued to exploit the Indian people. Sales of British textiles to India helped boost the British economy, and at the same time, Britain imported Indian products such as cotton, tea, wheat, and rice.
In claiming India as a colony, Great Britain also wanted to assert its mission of exporting their supposedly better culture to the rest of the world. As they considered themselves a superior race, the British felt a moral imperative to improve the welfare of the people under their rule. The Indians, of course, wanted home rule—and eventually, after World War II, they achieved this goal.