A 'peer-to-peer' network is a network of computers that are interconnected without passing through a central server. For example BitTorrent, BitCoin, Tor the browser are all examples of technologies that leverage this P2P architecture.
"Decentralized database" means that there is not central or singular copy of the database or the data in it. All the nodes ( i.e., the computers in this network ) have a copy of the entire database, the Blockchain.
Centralization in computing world is a very traditional form of design and architecture. With the advent of BitCoin among other things, this has changed in the recent years.