Decentralisation can apply to lots of things.
As Vitalik Buterin once layed out, it helps to see decentralisation as having multiple dimensions, in his view these three: technical, political, and logical. A technically decentralised network with a single developer influencing its progress is politically centralised. And if all nodes have to share the same data (the modus operandi of blockchains) it is logically centralised.
I see the purpose as reducing imbalances of authority and power, as much as is possible.
I guess I'm most interested currently in how it applies politically and technologically.