Damned if I know, not really. But at least I have a vague idea now, after puzzling through this explanation given by Edward Snowden to ACLU lawyer Ben Wizner. Read the whole thing here.
ES: It’s basically just a new kind of database. Imagine updates are always added to the end of it instead of messing with the old, preexisting entries — just as you could add new links to an old chain to make it longer — and you’re on the right track. Start with that concept, and we’ll fill in the details as we go.
BW: Okay, but why? What is the question for which blockchain is the answer?
ES: In a word: trust. Imagine an old database where any entry can be changed just by typing over it and clicking save. Now imagine that entry holds your bank balance. If somebody can just arbitrarily change your balance to zero, that kind of sucks, right? Unless you’ve got student loans.