The DC Comics' Extended Universe Brain Trust is a group of individuals that determine overarching plots throughout the DC Comics Extended Universe and oversee the "sandbox" in which Directors and Writers "play in" when developing films.
The group consists of Zack Snyder and wife Deborah Snyder, Producer Charles Roven, DC Comics Chief Creative Officer Geoff Johns and Warner Bros. Executive Vice-President Jon Berg. According to Roven, "I think also very much involved in that brain trust is Jon Berg, who is the executive vice president at Warner Bros. I would say the Snyders, myself, Jon Berg, and Geoff Johns would be sort of that Brain Trust… I’m working with great people. They’re all really great people. And not that we don’t—there are many times we agree, and there’s many times we don’t agree [and] we work it out".
The Brain Trust naturally evolved after the release of Man of Steel, the first film in the DCEU. It was put together by Warner Bros. so that an interlinking movie universe could be established that had an overarching story, but still allow film makers to make the movies they want.
The DCEU Brain Trust is similar to the Lucasfilm Story Group, which oversees creative direction and control over all Star Wars media, ranging from comics, TV to the films.