What is a cryptographic hash function?

A function that turns any input data into a fixed-length string (its "hash") that acts as a unique fingerprint of that data.

You feed in any amount of data — a name, a file, a whole block of transactions — and the algorithm outputs a fixed-length string such as a 256-bit value (SHA-256 is a common one). That output is a compact identifier for the exact input. Change even one character of the input and you get a completely different, unpredictable output. Hashing is the single most important primitive in a blockchain: it is how blocks are fingerprinted, how they are linked together, how mining puzzles are posed, and how addresses are derived. Understanding "same input gives the same hash, different input gives a wildly different hash" is the foundation for everything that follows.

Go deeper:

• Cryptographic hash function — Wikipedia — the core primitive: fixed-length fingerprints of arbitrary input.
• SHA-2 — Wikipedia — the family that includes SHA-256, the hash Bitcoin uses.