Blockchain isn't magic. It's math.
The current implementations of blockchain relate to cryptocurrency, like Bitcoin or Ethereum. So let's go with that as an easy way to describe the magic - er, math - of blockchain.
Generating cryptocurrency is like a gold mine. There's a mountain (the public ledger aka blockchain), and a bunch of gold nuggets (mathematical challenges) are buried in that mountain. Finding each nugget (solving the challenge) leads to finding more nuggets (moving on to the next challenge). But only up to a point. Because, like mines, cryptocurrencies are finite. Why? Blockchain.
Each step of the process of digging up the nuggets gets validated by a cryptographic algorithm, like an assessor who measures the size and weight of the gold nuggets you bring in after a long day of mining. No single assessor is given the power to validate all of the gold nuggets in the world. They group together and all have to agree, which is where the public ledger comes in. Each assessor shares their information by adding their "yup, it's gold and here's how much this nugget is worth" message on to one another's assessments that get logged in the ledger. The latest validation is added to the previous ones, forming a daisy chain of "yups." That chain links together all the available validations to prove you did, indeed, uncover a bunch of gold nuggets that the group of assessors agreed to validate.
Maybe "chainlink" didn't sound sexy enough. Instead, it's called "blockchain." Rather than simply issue a certificate of authenticity/value, which could be stolen or forged, the blockchain is made up of chunks of cryptographic algorithms that act as the authoritative "yup" to prove your mining efforts paid off. The act of mining cryptocurrency is known as...wait for it...cryptomining.
Cryptomining is like digging up all the gold nuggets from all the mountains. The value of cryptocurrencies is like any commodity. It's determined by how much people are willing to pay for it. Generating each "coin" is computationally expensive (translation: it takes a lot of horsepower) because the chain of algorithms is long and the math puzzles are intentionally hard to make sure the results are rare. The rarer the commodity, the higher its value. Blockchain accomplishes this by enforcing the difficulty by length and distribution of its structure. Thus, mining cryptocurrency is slow and methodical.
This is why bad guys have taken to hiding cryptomining scripts and programs on compromised systems. The more horsepower they can throw at mining operations by hijacking your computer, cell phone, TV, or other Internet-connected devices, the faster and more coins they can yield. The blockchains don't care who finds their associated coins (e.g. Bitcoin, Ethereum, Monero, etc.) or how, it only matters that they're found.
So, simply put, blockchains are distributed chunks of data that, when pieced together, validate information of value. Really, that's all. No magic required.