A blockchain is a way to ensure that accounting rules are followed without have any central authority enforce them. It does this by requiring that anyone trying to forge a transaction that breaks the rules has to compete in a very hard computational puzzle solving competition with all the participants trying to obey the rules. Unless the cheat can control more than half the available computer power on the network, they will almost certainly lose.
The key idea behind this is a hash function. A hash function is a function that summarizes a much longer piece of information, producing a number that is quite short, but extremely difficult to compute if you don't have the original information. Every ten minutes, the "mining" nodes of the blockchain network collect together a bunch of transactions that obey the rules, and try to create a new block. The block consists of the hash of the previous block (hence block chain), the new transactions, a special number, and its own hash.
The special number is the clever part. It has to be chosen such that the hash of the block has some special property. In the case of Bitcoin, the hash has to have a certain number of leading zeros. This is very hard to do - there is no way to solve the problem except to try numbers at random and see which ones work. The difficulty of choosing the special number is tuned such that it will take the entire power of all the machines cooperating to enforce the rules approximately ten minutes to do.
This is an expalanation of how it works not why it is valuable.
Sorry for mistake. I think, blockchain derives its unique value from the fact that despite its lack of official backing or wide acceptance, it has generated an ecosystem in which many people are willing to trade and accept it. In fact, some perceive blockchain to be more valuable, or more useful, than other currencies in that it is a better option for certain purposes, such as seamless digital transfers and use across borders. Also, because there is a cap set on the total number of blockchains that will ever exist, the currency cannot be devalued through inflation as others can. Finally, a key benefit of bitcoin is known as “censorship resistance,” its ability to be used for transactions that could normally be censored by other payment networks.
For that blockchian has a value for world economics