Nowadays most of the money is just in the form of numbers. So there is a possibility that the same money can be used for multiple transactions. This problem is called as “Double Spending”.
To avoid this, banks keep a ledger to keep track of all the transactions essentially acting as a Centre. Hence our conventional money is called as Centralized Currency.
Some computer scientists were not satisfied with a third party(bank) keeping track of transactions. This is when Satoshi Nakamoto comes in and proposes and entirely different solution where there is no 3rd party involved(decentralized currency). BITCOIN
Decentralized currency is like Internet. There is no one entity owning it(yet). The deal with Bitcoin is that all the transactions are public and the ledger recording those transactions are public.