A mandate is an official command or a go-ahead. When a politician wins an election by a wide margin, that's a mandate to implement her ideas.
A mandate gives authority. If the government gives schools a mandate to test more, then the schools had better give more tests. People who work for the Peace Corps have a mandate to help various countries with things like getting clean drinking water. A politician who believes in higher taxes and then gets elected considers that a mandate to raise taxes. When you have a mandate, it's like a ticket to get something done.