Okay, maybe you read through the site, maybe you didn't. Here is the absolute bare-bones explanation of how Bitcoin works, aimed to describe how the technology works in as few words as possible:
Bitcoin is a digital money that uses a shared ledger (digital file showing which accounts hold how much money) across thousands of computers across the world. This ledger uses cryptography to move funds from one account to another. Each user has a private key, which is like a password that can authorize funds to be moved from their account to any other account. This is a one-way process, so it cannot be reverse. Basically, your private key releases the money from your account into another account that you specify (such as a friend's account or a store's account). This release is distributed to the network of computers to update the ledger, but there is a process involved before the ledger can be updated.
Some users, called miners, take all of these floating fund transfers and bundle them together into a block of data. From here, all miners are competing to solve a difficult mathematical equation involving this transaction block, and whoever solves the problem first gets to reward themselves with a small reward in Bitcoin freshly minted. The more people that participate in mining, the more difficult the mathematics problem gets, which results in the solution being found every 10 minutes or so, and then the next batch of transactions occurs. Each new batch of transactions is the next wave of transactions updated on the ledger. Every 210,000 blocks that are solved also cuts the reward in half, so there will only be 21,000,000 Bitcoin ever created (but don't worry, you can break a Bitcoin into 100,000,000 sub-units, called a Satoshi) in the year 2140.
By implementing a system that adjusts its own difficulty, uses solid cryptography, and has no centralized authority that can be tempted to profit from the system, we are experiencing a monetary system that is similar to gold, except it operates across the internet and be used between any two people in the world. This is a truly magical and fascinating technology that has the potential to change the world by introducing a monetary system that is border-less, robust, low-friction, and open for innovation by all.
If you liked this, you should give the full tutorial a try: What is Bitcoin?