Well, on one level it simply means 'to communicate'. 'How can we communicate our message to the public effectively?' But as Alena said it also means 'communicate in a way which is understood' AND also 'communicate in a way which is convincing and believable'. So you could say: "How can we communicate with the public so that they understand our message and believe it?"

It means 'make someone understand'. "How can we make the public understand our message?"