In a decentralized network, data is not stored or administrated by a private server. Instead, the blockchain is redundantly stored and monitored by many nodes, distributed amongst a web of individual machines with different owners that perform continuous consensus on the validity of changes to its state. If this sounds like you’re being asked to trust a bunch of strangers to behave honestly, it’s actually quite the opposite: there are mechanisms in place to reward nodes which align themselves with network consensus, and penalize those which do not. (See the Proof of Stake section for more on OMG’s specific enforcement mechanisms)
Centralized networks require trust in a central party, which will maybe - even probably - act responsibly. However, centralized systems are necessarily opaque and gated, and centralized databases are vulnerable to attack because they present a single point of entry for bad actors looking to steal or manipulate that data. In contrast, decentralized networks are transparent in that every state and every state change (i.e. every balance and every transaction) is stored on a shared ledger which can be viewed by anyone, or are obscured in a way that makes voluntary provable traceability possible where necessary, so there is no need to trust the word of a central authority.