This seems like the neverending story, and because I’m tired of it I want to share my understanding:

• Association: Used when one instance should send a message to another instance. There’s no a whole / part relationship. In Java this can be an instance calling another instance’s methods. Examples of this can be a Customer and its persistance mechanism (DAO – data access object). They just send messages between each other.
• Aggregation: Used to represent a whole / part relationship. The creation and destruction of child objects is not controlled by their parent. For example, a Binder and its sheets. You can destroy your binder and save your sheets for later usage… or for another binder.
• Composition: Like an aggregation but the life span of child objects is controlled by their parent. For example, a Notebook and its sheets… If you create a notebook, you need to create sheets to fill it with. If you destroy your notebook you will destroy all your sheets. You know you have a composition when you no longer need the child objects once the parent has been destroyed.