"In those days the big U.S. labels didn't have any particular interest in the Latin market"

This quote by Ruben Blades is describing the music industry in the past. In the past, the big U.S. labels did not have any specific interest in the Latin music market. This was likely due to the reality that Latin music was not as popular in the U.S. as other categories, such as rock and pop. As a result, Latin artists had to count on smaller sized, independent labels to get their music out to the general public. This absence of interest from the huge U.S. labels implied that Latin music was not as extensively readily available or as popular as it might have been. Fortunately, this has actually altered over the last few years, as the big U.S. labels have actually started to acknowledge the capacity of the Latin music market and have actually started to purchase it. This has allowed Latin music to end up being more commonly readily available and popular, and has permitted Latin artists to reach a broader audience.