When things cohere, they come together in a meaningful way. It wasn't until we won a game that our team finally cohered, and we actually felt like a unit.
Co- means "together," and here is from the Latin haerēre, "to stick." Put them together and you have "to stick together." When people work together on a project, it's important that their ideas cohere, otherwise the work can seem disjointed and awkward. The beauty of the dance was in the timing: everyone was so in step that they seemed to cohere into one great mass of humanity. If the president's staff doesn't cohere into a cohesive unit, his policies will never come together either.