Regarding the CPB
The Corporation for Public Broadcasting (CPB) is a private non-profit corporation which is chartered and funded by the US Feds to promote public broadcasting. It was created in 1967 when Johnson signed the Public Broadcasting Act. In 1969 the CPB decided to start its own network, PBS. The CPB now provides some funding for PBS and member stations of NPR, and that includes WBFO.

Regarding WBFO and NPR
National Public Radio is a syndicated national news provider. To air their programming, WBFO must pay NPR a substantial fee for Morning Edition, and All Things Considered. The CPB provides an operating grant to WBFO to help pay for these shows.