In order to get a better idea of what Blockchain technology is all about it's a good idea to take a look at Bitcoin: A Peer-to-Peer Electronic Cash System, published in 2008 by Satoshi Nakamoto. (Nakamoto apparently being a pseudonym of some person or group of people.) This paper is the origin of the bitcoin cryto currency, and the first representation of the blockchain concept.
The basic idea is for digital signatures to be used for electronic cash transactions without the involvement of a third party institution. Double spending is prevented through use of a public ledger that hashes timestamped transactions.
On the second page of his (her?) paper, Nakamoto demonstrates the basic idea of electronic currencies in a chart that shows how use is made of public and private keys.
The trouble is that an institution must issue an electronic coin for each transaction in order to avoid double spending. Nakamoto's proposed solution is to use a timestamp server to hash a block of items and publish it. Each timestamp includes the previous timestamp in its hash.
The integrity of the chain depends on CPU power, since altering any one block would require altering all blocks in the chain, and then catching up with new genuine blocks. The very fact that computing power generates Bitcoins protects the blockchain against attacks:
"If a greedy attacker is able to assemble more CPU power than all the honest nodes, he would have to choose between using it to defraud people by stealing back his payments, or using it to generate new coins. He ought to find it more profitable to play by the rules, such rules that favour him with more new coins than everyone else combined, than to undermine the system and the validity of his own wealth. "
While the blockchain model makes transaction public it maintains privacy by keeping the identity of the parties anonymous. The paper includes another chart illustrating the difference between public trades on a stock exchange and blockchain transactoins: