If you have to pass a test to graduate, the test is important. It is vital, necessary, crucial.
The President is the most important person in the country. Children are important to parents, and parents are certainly important to their children. Different people think different things are important: a new movie might be important to you because you care about it a lot, even if it's not important in the same way as food and water. People often say "Good study habits are important" or "Communication is important." Important things matter.