The part that confuses me is exactly how this is going to be accomplished. I’m still trying to understand what blockchain is and how it works.
Simply by storing a random number on your phone or PC. It's a 32 byte random number, and only you know the value. Run that number through a function to get your public key, you can give that to everyone. Anyone can send you messages securely by encrypting them with your public key (you decrpyt with your private key).
But that's not blockchain. Instead of encrypting (with public) and decrypting (with private key) it uses the same functions with the opposite keys. You sign with your private key, and everyone else verifies the signature with your public key. That's still not quite the blockchain. The blockchain contains a hash of the public key because it is shorter and that adds a bit of security. When you want some crypto money you create a private key in your phone or PC wallet SW. The SW stores the private key securely and prompts you to make paper backups. The SW calculates the corresponding public key. The SW hashes the public key into an address. Now you can get payments made to that address.
When you want to pay someone else (their address) you have to prove you are the "owner" of an address on the blockchain that previously received a payment. To prove that, you sign a transaction with your private key. Then all the miners verify that transaction with the public key which you reveal with the transaction. If the verification succeeds they hash the public key to get the address to make sure it matches the one on the blockchain that you claim that you own. Then the transaction is added to the blockchain wherein you send some or all of the value assigned to your address to a new address (the person you want to pay) You might also receive "change" back to a new address created by your wallet SW. That's also stored in the blockchain in that transaction.
The blockchain is simply a record of the transactions taking money from one or more addresses and sending it to one or more destination addresses. All addresses are "owned" by someone who has the private key. Unless the private key was lost or the address was simply concocted. In that case the money that was trasnferred is lost forever (that helps keep the price of bitcoin high).