The term "World History" is a bit of a misnomer. Certainly, as other posts have indicated, its important to consider the history of other cultures and countries; doing so can only help our international situation today, but this consideration must be done in relation to one's own. Done properly, a profounder understanding of different cultures through time can occur. It is not to imply that one particular history is "true;" what it suggests is the ability of the student or scholar to appreciate all aspects of the time, place, and culture when events occurred. "World History" then, would be the understanding of events, or causes and effects, from multiple viewpoints. But to have a viewpoint, one must start with one's own.
Studying the "History of the World" may be tacitly suggesting the abandonment of one's own cultural perspective in favor of another; however, to understand fully why we are where we are, inquiry must be made into causes and effects with a minimum of political correctness. The study of any history should concern itself with facts. It should seek to establish what was true.
World history has been growing, because people are more interested in the world. The world is far smaller than before due to globalization. Nations are connected. Hence, it behooves people from one side of the globe to understand another person from the other side of the world. Also, I suspect history is growing, because most histories were written from a western perspective. Now people are aware of this. Edward Said made this point a long time ago and people are catching on. This point is important, because people are looking for world histories from the perspective of others. For example, how does an African see world history or a Asian or a South American? These are all valid and interesting perspectives.
Some wise man said "bigger the island of knowledge, longer the shore line of enquiry." The biggest reason growth of history has been the increase in the total accumulated knowledge about it as more and more information is uncovered and ascertained. With this increase in total available store of world history knowledge, the interest in learning more about it has also grown. Also people have a much wider range of topics available to enquire about.
Growth of field of world history has also been aided by development of newer and better methods for historical research.
If talk about growth of world history in comparison of history in general, the main reason for it is the growing awareness and interest of people about affairs round the world rather than within their immediate region.