The process is relatively simple, but as we say it involves more people. Now Mariano and Luis are not alone, and will be part of a large group of users who are responsible for verifying that the entire process occurs as it should occur.
If Mariano wants to withdraw a bitcoin from his account to give it to Luis, he first notifies everyone with a peculiarity: nobody knows that Mariano is Mariano and that Luis is Luis. They only know that from a digital wallet (what would be a bank account) you want to transfer that amount (which is known) to another.
Mariano, therefore, warns of his intentions, but without revealing his identity: "Hey, guys, I want to send a bitcoin from my wallet to this one, please update your account books!" By sending that message, all users of that network first verify that Mariano the source portfolio has enough money to send it to the destination portfolio. If so, everyone writes down that transaction, which becomes complete and becomes part of the transaction block. Of course: they are not yet registered in that database permanently.
As time goes by, more and more transactions are completed and passed to that block, which has a limited capacity that depends on the structure of the blockchain and the size of each transaction. When a block no longer supports transactions, an important moment arrives: to "validate" or "seal" it, which is what users do when they do bitcoin mining.