Its complicated. If you dont have a bank that manages all the money, you really need to have something transparent. Something everyone can understand. A list of all the coins there are, and how they have moved around from the beginning. A list stored on lots and lots of different systems. This is what some person called the blockchain. A blockchain is essentially a shared ledger. Thousands of computers can keep a copy of the same transaction history. Whenever coins move from one person to another, the network updates the ledger.
The advantage is that no single person owns or controls the database. The network itself verifies the transactions.
For our project we do not need thousands of computers. We can start with a single database on a single server. It will not be decentralized, but it will allow us to explore many of the same ideas.
In this experiment, I effectively act as the central bank. I decide how many coins exist, I maintain the database, and I can verify transactions. This means that trust in the coin is based not only on the software, but also on the trust you place in me.