Delegation is giving specific tasks and responsibilities to someone else, usually a junior. For instance, if you are an office manager and part of your work is to put new names into a database, you could delegate that to a trainee. Executives are often advised to "learn to delegate" because it's easy to take on too much work rather than share the burden.
Decentralisation is on a much bigger scale. It means moving power and authority away from the centre (usually national government) and handing it over to bodies or organisations outside the centre, especially regional organisations. In politics, this might mean that an area of policy - social housing, for instance - that used to be decided by the national government, is now the responsibility of local government, local councils and so on. The verb "to decentralise" is also quite often used, as in "We need to decentralise decision-making."
Decentralisation is on a much bigger scale. It means moving power and authority away from the centre (usually national government) and handing it over to bodies or organisations outside the centre, especially regional organisations. In politics, this might mean that an area of policy - social housing, for instance - that used to be decided by the national government, is now the responsibility of local government, local councils and so on. The verb "to decentralise" is also quite often used, as in "We need to decentralise decision-making."