"Big" is a slang word for "popular" in the business community, particularly the entertainment industry. It's not uncommon for a musician or band to fail to attract notice in their own country, but then relocate to another place and become popular there. Legendary guitarist Jimi Hendrix and Chrissy Hynde of the Pretenders both moved to England and achieved popularity there before becoming "big" in the U.S. The same applies to genres of music and other art. Reggae is much "bigger" in--well actually almost anywhere but America.