A centralized payment verification system, like Paypal or any number of financial institutions, only considers payments "valid" if they come from within the organization. A single organization is responsible for verifying the truth of statements (with a statement being "Bob sent Alice $50" and the like). This means that there is no mechanism of agreement on transactions required.

By contrast, decentralized systems like Bitcoin, Ripple and Stellar all must come to agreement on which transactions are valid, without a centralized authority to confirm their truth. Proof-of-Work, Proof-of-Stake, Tendermint and SCP (Stellar Consensus Protocol) are each different solutions to this problem.

Pros of a centralized system:

• No need for a mechanism of agreement, such as mining or consensus
• Lower operational costs

Cons of a centralized system:

• There is a single point of failure. If the central authority goes down or offline, the entire network is compromised.
• Centralization can post ethical issues of who controls information and money.It opposes the ethos of a neutral net.
• Creates a closed network, meaning that entities can only join the system with the consent of the centralized authority
• May only serve the interest of the centralized authority.
• Does not allow for p2p interaction/payments