What it is: A federal government is one in which power is divided between one central government and several regional governments.
What it means: This is the case in (for example) America, Switzerland and Malaysia. 'Federal' can also be used to describe a union or association of states or groups which are all self-governing: some people like the idea of European countries being linked in this way. People who are looking for ways to achieve world peace have sometimes talked of a 'federation of the world', to which every country would belong. This ideal respects the individuality of every country, yet recognises that they must work together to deal with the world's problems. Such a federation would still need a 'head office' to co-ordinate things. The history of the United Nations, the nearest equivalent to a world HQ, shows that nations often find it very difficult to pull together. The existence of armies and weapons makes trust and co-operation extremely difficult, too.
Think about it: A federal world probably needs peoples, not politicians, to promote it. It might grow up from the grass roots more easily than be imposed from the top. If the entire planet faced disaster (man-made or not) federalism (and disarmament) might turn out to be the only answer. Can the way people from other countries rally round to help victims of earthquakes and other natural disasters be built on to create a more 'federal' view of things?