How the blockchain technology helps achieve elimination of intermediaries is by replacing trust that intermediaries bring to the table with cryptographic proof by the use of CPU computing power.
This cryptographic trust is built into Bitcoin through a wallet, a public key and a private key in the program.
Anyone can create a Bitcoin wallet for free by downloading the Bitcoin program. Each wallet contains a public key and a private key.
The public key is like an address or an account
number via which any person can receive Bitcoins.
A private key is like a digital signature via which a person can send Bitcoins. The name suggests that private keys should be only held and known by the owner and public keys can be shared with anyone for receiving Bitcoins. That is where you would have heard in the news about Bitcoins being lost either due to a private key not being accessible or stolen by hackers.
Owners of Bitcoin addresses are not explicitly identified, but all transactions on the blockchain are public.
Since the inception of Bitcoin in 2009, each and every transaction that has occurred is stored in a ledger, which is considered immutable, non-tamperable and irreversible.
Bitcoin transactions are verified via telecommunication network nodes through cryptography and are then recorded in a decentralized distributed ledger called blockchain. This is one of the distinguishing aspects of Bitcoin from some other crypto assets, where there is centralized exchange (like the stock exchange) through which all transactions need to be routed or validated.