Blockchain is database architecture. It involves multiple computers in order to ensure the consistency of data. That's why blockchain is called a distributed database. All the pieces of data are encrypted with a highly tamper-resistant algorithm.
Long, but simple answer:
Let's try an example. You buy every day from a good old local grocery store. You have a personal account with the grocer, so whenever you need anything, the grocer gives you a credit by making a record in a book. When you come to the store on your payroll day, the grocer checks his records and tells you how much you owe. The grocer's record book is a metaphor for a traditional database.
Now imagine a blockchain-powered grocery store where each buyer has their own record book. Whenever any of the customers makes a purchase, every single person present in the store opens their book and makes a record. In this store, none of the books is considered more authoritative than the others. When it's time that you should pay your credit, the amount told by the grocer is checked against all the books. So if the grocer's book is lost or damaged, you due amount is nevertheless known.
To make it more true-to-life, let's mention that the grocery store has its own currency, and whenever you need to save any transaction to the record books, you pay a penny it that grocery store currency.
And, finally, all the records in all books are stored encrypted, so it's hard to fake a record. Even if anyone tries to, their book gets destroyed, and the information stored within the community remains consistent.