TL;DR

A blockchain is a tamperproof collection of data structures (blocks) that is replicated across a network of computer nodes. These blocks are connected together (chained) using an algorithm that prevents tampering, secured by the consensus of all nodes on the network.

ELI5

Imagine you have a notebook that you use to keep track of the video games that you and your friends own. You want to make sure that you keep the notebook up to date with who owns what game and which games have been borrwed by which friends. If any friend wants to borrow a game, a note is written in the notebook to describe which fiend borrowed which game. Your friends maybe don't completely trust that you will always record every note accurately in the notebook, so they ask to make a copy of the notebook for themselves and be told whenever there is a new note written in the notebook. You and your friends can now routinely compare your notebooks to make sure they are always the same. If you or any friend ever writes a note in the notebook that is different from the note in you or your friends' notebooks, it will become obvious that this note is verifiably invalid. This is similar to how a blockchain works.

As a beginner

Without a blockchain, storing data in a data storage system (e.g., the database of a bank) requires that you trust the owner of the system to not tamper with the data. This is because the owner of the system can change the data in the system at any time since they own and operate that data storage system. A blockchain is a publicly visible data storage system that is designed to prevent tampering of the data by replicating the data across a large number of connected computers and using a special data validation technique to verify the data in one computer matches the data in all other computers such that tampering becomes immediately apparent. This means that the data in the blockchain does not need to be trusted for accuracy by any one computer and instead can be independently verified for accuracy by anyone through running the special data validation technique themselves.

How is it tamperproof?

The algorithm used to chain the blocks together uses what is called a hash function. This hash function uses inputs from the previous block to sign the next block. This means that if any data in the previous block is changes, the hash of the previous block changes. This in turn changes the hash of the next block, and so on. This means that if any data in any block is changed or tampered with, the hash of every block after it changes. This is how the blockchain prevents tampering because any change to previously agreed upon data (via the network consensus) would invalidate the chain of blocks following the tampered data.

How hash algorithms work

A hash function is a one-way function that takes an input and produces a unique output. The output is called a hash. The hash is a fixed length series of characters that is unique to the input. If the input changes even slightly, the hash output changes significantly. If the input is the same, computing the hash output over and over is always the same. While a duplicated output for 2 or more unique inputs is theoretically possible (known as a hash collision), the statistical likelihood of this happening is so infinitesimally small that it is considered de facto impossible.

E.g., Bitcoin

The hash function used in Bitcoin is called SHA-256. It takes an input of any length and produces a 256-bit hash. The hash is always 256 bits long, regardless of the length of the input.

What is stored in a block?

A block contains a header and a body. The header contains metadata about the block, such as the hash of the previous block, the hash of the current block, the timestamp of the block, and other data. The body contains the actual data that is being stored in the blockchain. This data can be anything, but is often a collection of transactions of some kind. For example, in Bitcoin, the body of a block contains a list of transactions that have occurred since the previous block. The type of data stored in a block depends on the type of blockchain, some chains are more focused on token transactions and others are more focused on data storage.