The film industry moved to California generally, and Los Angeles specifically, for two primary reasons: a) Weather, and b) Thomas Edison.
The latter is perhaps the more interesting story.
The famous inventor, Thomas Edison, along with his New Jersey companies, held a variety of patents related to early motion picture technology, including the Kinetoscope, one of the earliest movie cameras, which he patented in 1861. Edison used these patents as a legal tool to control the production and screening of early films.
These patents applied to the creation of movies, and the technology used to exhibit them in movie theaters. As a result, he was able to pressure other filmmakers into a business collective in which he held significant sway. This collective eventually became the Motion Picture Patent Company, also called the Edison Trust, in December 1908. It held 16 major film patents.
As a result, the MPPC, had a practical monopoly on the production, distribution, and exhibition early movies.
Take the example of Eastman Kodak, which owned the patent on raw film stock. Kodak was a member of the MPPC, and as a result only agreed to sell film stock to other member of the group at the time.
The MPPC used court action to prevent the unauthorized use of cameras, projectors, film stock, and so forth, According the book, “Final Cut” by Steven Bach, the MPPC even went so far as to hire organized-crime-affiliated enforcers to enforce patents, sometimes going so far as to destroy equipment of competing companies not members of the MPPC.
The MPPC became the most powerful force in the US film industry.
It required producers and exhibitors to use its patented equipment, and levied a $2 per week license fee to all cinemas of the time. The Edison Trust/MPPC required a fixed price of admission, and also banned film credits for actors and actresses.
The group effectively controlled in large part what films were seen in the United States, often blocking imported films.
As a further result of the above, many of the smaller independent film companies left for California, which is about as far from New Jersey one can get without diving into the Pacific Ocean. As well, California courts of the time were less friendly than those in New Jersey to these sorts of patent-claims. As well, cross-continental legal-enforcement was somewhat more difficult as well as more expensive.
The founders of some of these smaller, independent production companies included early producers like Carl Laemmle, Adolph Zukor and William Fox. Their companies, eventually relocated to Los Angeles, eventually became the Hollywood studios we know today as Paramount, Universal and 20th Century Fox.
On the practical side is California’s geography and environment.
The weather is conducive to year-round shoots, with very few rainy days. One can film outdoors most days of the year, something impossible on the East Coast. The area also has diverse topography, deserts, beaches, forests, and mountains are all within reach, allowing filmmakers to simulate locations almost worldwide within a day’s drive from Los Angeles.
You can learn more about this interesting history here, among other places:
Charles Musser. Before the Nickelodeon: Edwin S. Porter and the Edison Manufacturing Company. Berkeley: University of California Press, 1991.
Briley, Ron. "Reel History: U.S. History, 1932-1972, As Viewed Through the Lens of Hollywood." History Teacher, 1990.
Cameron, Kenneth M. America on Film: Hollywood and American History. New York: Continuum, 1997.
Rosenstone, Robert A. History on Film/Film on History. New York: Longman/Pearson, 2006.
Richard Maltby, Hollywood Cinema. London: Blackwell, 1995.