It refers to the idea that the whole always equals the sum of its parts. Well, that idea is wrong. As we all know, the whole can be more than the sum of its parts – or less. Consider this statement: if each bank is safe and sound, the banking system must be safe and sound as well.
By now, we have learnt the hard way that this might indeed be a fallacy of composition. Let me give you just one example. Imagine that a certain asset suddenly becomes more risky. Each bank that holds this asset might react prudently by selling it. However, if many banks react that way, they will drive down the price of the asset.