In cryptocurrency, a ‘witness’ attests to the authenticity of a specific transaction in the form of a signature.
For a Bitcoin transaction, the witness is the content of the signature scripts, which is what proves the transaction is authenticated. Segregated Witness (SegWit) is an upgrade of the Bitcoin protocol that includes a change in the transaction format that increases block capacity and protects from transaction malleability. It was also intended to speed up the validation process by removing witness data from transaction data.