You should think of bitcoin as two parts: a monetary unit, and payment processing network.
The payment network is a decentralized network of random joe sixpacks that run some open source software. This software listens for transactions on the network and bundles them up into little squares. These squares are then stacked onto each other, one on top of the other. As you can imagine, the squares deeper in the pile get harder and harder to pull out and change because of the weight of all the newer squares on top of it. This gives historical transactional security. The farther back in the stack, the more secure they are.
Each time Joe Sixpack stacks a bundle of transactions, he gets paid for his work in at least one of two ways: transaction fees, and monetary inflation (money created out of thin air – but don’t worry, there is mathematical regulation that prevents runaway inflation, and actually stops in decades in the future).
The monetary unit is literally just an accounting entry that says acount ABC has X bitcoins available for spending. Each transaction that is made creates a sort of bank check that says “pay to the order of account XYZ in the amount of Y bitcoins” and the owner of the account signs that check with a counterfeit proof pen. This pen has a special property in that it can be verified by anyone in the network. Joe Sixpack uses this property to verify authenticity of transactions as he bundles them into stacks.
Back to inflation… There will only be 2.1 quadrillion monetary units (satoshi) or 21 million bitcoins. This is guaranteed by simple math like “divide 50 in half every four years until you reach zero”. At this point, no more bitcoins can be created. And we’ll never really reach that number in circulation because many people have already lost hundreds of thousands of bitcoins to forgotten passwords, formatted hard drives, and crashes with no backups. These losses to attrition will continue throughout the life of Bitcoin so the monetary units in circulation will continue to go down over centuries.