What is it?
Blockchain is the software behind many different cryptocurrencies that enables individuals to transact safely and without the need for a validated middleman.
This technology can be used for a wide range of different tasks, but as far as the crypto industry goes, Blockchain serves as a distributed ledger, a decentralized global network for fast, cheap transactions, as well as a platform for new and other software programs to run on.
How does it work?
Let's say you've just transferred Bitcoin to a friend. After clicking the send button from within your wallet, your transaction joins all of the other unconfirmed transactions on the Bitcoin network in the memory pool (aka mempool).
In order for your transaction to be successfully completed, it needs to first be validated by at least one miner, and generally, a transaction will need to be verified at least 6 times before it's added to the next block to be added to all of the other blocks on the chain (hence the name Blockchain). What information is stored in that block? Just your public key (wallet address), your friend's public key, and the transaction's amount.
Side note: miners don't work for free (for a simple explanation on mining, click here). They're compensated for their hard work - either with newly mined Bitcoin, or with Blockchain transaction fees, the latter of which you, the transactor, decide.
Once your transaction is on the Blockchain, anyone anywhere in the world with a working internet connection will be able to view it, along with your wallet's history, since the Blockchain is a public ledger.