What is a Blockchain?
A blockchain can be seen as a special kind of database which is replicated through multiple nodes across the internet (usually thousands of them). This makes this database highly available and censorship-resistant. Anyone can participate in the network and store a replica in their computer!
However what makes this database so special is the way it stores the information: it is contained in blocks of data which are appended at regular intervals. Moreover, these blocks are "chained" sequentially by referencing the last block of the sequence in a special way: using a cryptographic function known as hash function.
What is a "hash"? A hash is commonly used to refer to the value returned by a cryptographic function which maps data of arbitrary size to data of a fixed size. This function has the property of returning a completely different values (hashes) if the input data changes. In a blockchain a hash of the previous block is included in the current block; thus any change in any block will invalidate the subsequent blocks, since the hash of the modified block will not match with the value stored in the subsequent one (and so on and so forth).
As a result blockchains are tamper proof, since any modification in the data contained in a block would invalidate all the data stored since that block was generated.
Another important property is its transparency: anyone participating in the network (this is, a network node) validates every stored block and helps broadcasting them to other peers. On the other hand public blockchains are available to anyone to read and check its contents.