Definition
A hash is a fixed-size output produced by a cryptographic hash function from any arbitrary input. Key properties include: deterministic (same input always produces same output), one-way (cannot derive input from output), and avalanche effect (small input changes produce completely different outputs).
In Bitcoin mining, the double SHA-256 hash of the block header must be below the target value. Since there is no way to predict the output, miners must try billions of inputs (changing the nonce) to find a valid hash. This is the computational work in Proof of Work.
In Simple Terms
The output of a cryptographic function. Miners search for block hashes below the difficulty target.
The output of a cryptographic hash function. In Bitcoin mining, miners seek a hash of the block header that is below the difficulty target.