There are two ways to answer this question.
One is to ask why the rise of the British Empire was possible--what allowed it to happen. The major answer to this question is technological. During the Victorian Era, improvements in technology helped the British go farther and faster to trade. This was seen first with the clipper ships and later with steamships as they became more effective due to technological advances. Improvements in technology also gave the British the military means to do things like defeating China in the Opium Wars.
A second way is to ask why the British wanted to take an empire. Here, the answers have to do with economics, power, and prestige. Economics is the most important of these factors. It was economics that drove the British to take control of India and to fight the Opium Wars with China. It was the need to protect trade with this area (through the Suez Canal) that first got Britain heavily involved in Africa. Later, empire was seen as a source of military power and a large empire was seen as a source of pride. But the major underlying factor was economics.
So, you can say that the rise of the empire was caused by the technological changes that made it possible or you can say it was caused by the motives that made Britain want to pursue empire.