What does 'significant and strategic audiences ‘ mean?
The Broadcasting Board of Governors (BBG) is a United States government agency. Its goal is to "deliver accurate news and information to significant and strategic audiences overseas... and to serve as a trustworthy source of news and as an example of a free, professional press in countries that lack independent media."[1] It was previously a department within the United States Information Agency until 1999.

Question

Answer

In this context I would guess that "significant" refers to the size of audiences (i.e. it means more or less the same as "large") and "strategic" refers to their importance for whatever purposes are promoted. For example, it might mean that local journalists likely to report on news related to the US are particularly important (and so "strategic") audiences; they should have access to accurate information so that their reports in the local press (which will be "consumed" by a wider audience) are complete and reliable.