In simple terms, a blockchain can be described as an append-only transaction ledger. What that means is that the ledger can be written onto with new information, but the previous information, stored in blocks, cannot be edited, adjusted or changed. This is accomplished by using cryptography to link the contents of the newly added block with each block before it, such that any change to the contents of a previous block in the chain would invalidate the data in all blocks after it.
Blockchains are consensus-driven. A large number of computers are connected to the network, and to reduce the ability for an attacker to maliciously add transactions on the network, those adding to the blockchain must compete to solve a mathematical proof. The results are shared with all other computers on the network. The computers, or nodes, connected to this network must agree on the solution, hence the term "consensus."
This also makes the work of appending data to the ledger decentralized. That is, no single entity can take control of the information on the blockchain. Therefore, we need not trust a single entity since we rely on agreement by many entities instead. The beauty of this construct is that the transactions recorded in the chain can be publicly published and verified, such that anyone can view the contents of the blockchain and verify that events that were recorded into it actually took place.
One of the prime reasons blockchain is intriguing to businesses is that this technology is almost always open source. That means other users or developers have the opportunity to modify it as they see fit. But what's most important about it being open source is that it makes altering logged data within a blockchain incredibly difficult. After all, if there are countless eyes on the network, someone is probably going to see that logged data has been altered. This makes blockchain a particularly secure technology.
As noted, blockchain allows peer-to-peer and business-to-business transactions to be completed without the need for a third party, which is often a bank. Since there's no middleman involvement tied to blockchain transactions, it means they can actually reduce costs to the user or businesses over time.
When it comes to traditional banks, it's not uncommon for transactions to take days to completely settle. This is due to protocols in bank transferring software, as well as the fact that financial institutions are only open during normal business hours, five days a week. You also have financial institutions located in various time zones around the world, which can delay processing times. Comparatively, blockchain technology is working 24 hours a day, seven days a week, meaning blockchain-based transactions process considerably more quickly.
Another central reason blockchain is so exciting is its lack of a central data hub. Instead of running a massive data center and verifying transactions through that hub, blockchain actually allows individual transactions to have their own proof of validity and the authorization to enforce those constraints. With information on a particular blockchain piecemealed throughout the world on individual servers, it ensures that if this information fell into unwanted hands (e.g., a cyber-criminal), only a small amount of data, and not the entire network, would be compromised.
Lastly, cryptocurrency investors are tend to be really encouraged by the control aspect of blockchain. Rather than having a third party run the show, users and developers are the ones who get to call the shots. For instance, an inability to reach an 80% consensus on an upgrade tied to bitcoin's blockchain is what necessitated a fork into two separate currencies (bitcoin and bitcoin cash) more than four months ago. Having a say goes a long way with investors and developers.