Decentralization is the most important property of Bitcoin

Decentralization in Bitcoin refers to the extent to which power is dispersed between network participants. This is influenced by both the number of participants and the balance of power between them. Decentralization is desired because it makes Bitcoin more likely to have the following properties (from this post by Justus Ranvier):


 * The conditions of the scripts associated with unspent outputs will be honored. This means that if a user owns Bitcoins, they can't be spent by someone else.


 * No user's fraction of total Bitcoins will be diluted (in excess of the known inflation schedule).


 * When a user decides to spend their coins, they'll be able to do so within a reasonable time frame without requiring permission from a third party.

The more decentralized Bitcoin is, the less likely it is that some group of entities will interfere with a user's transaction or try to pass off invalid transactions as valid. Decentralization is a continuum, and changes to the level of decentralization are good or bad in proportion to how they change the probability of the above properties holding.

For instance imagine that Alice wants to send some bitcoins to Bob. If one group controlled all of Bitcoin's hashing power they could require any sort of criteria they wanted before they confirmed Alice's transaction. They could require that she identify herself, that she pay an extremely high fee, or that she prove that she paid the appropriate taxes on the money she's sending. If this group also ran all of the full nodes, they could process transactions that were invalid (in effect, changing the protocol) and transfer money between users arbitrarily or create unlimited coins to give to themselves.

Now imagine a much more decentralized scenario, in which one million entities each had one millionth of the total hash power, and each ran a full node. Although it would be theoretically possible for these entities to coordinate to prevent Alice from paying Bob, coordinating such large numbers of entities would be very hard, and it's unlikely that so many entities' interests align against Bob or Alice that they'd be motivated to tackle this coordination problem. The vast majority of them probably wouldn't care about this transaction at all, aside from the fees that it pays them. Similarly in a world of one million equally powerful entities, it is far more unlikely that they'll all (or almost all) conspire to spend other people's coins or create Bitcoins out of nowhere. As long as there are some honest nodes, they can sound the alarm to users that other participants are not following the rules of the protocol.

Note that decentralization being extremely valuable does not mean that we should always do whatever we can to increase decentralization no matter the costs. Decentralization is not infinitely valuable. The benefits of a reduction in decentralization should be weighed against the increased likelihood of the properties listed above being violated.