Homomorphic encryption is a form of encryption with an unusual property: you can perform calculations directly on the encrypted data, and when you decrypt the result, you get the same answer as if you had done the calculation on the original, unencrypted data. Ordinary encryption locks data so tightly that you must decrypt it before doing anything useful with it; homomorphic encryption lets a party who holds only the locked version still compute on it, without ever holding the key.
The practical appeal for machine learning is encrypted inference. A user can encrypt sensitive input, a medical image, a financial record, send it to a cloud service, have the service run a model on the ciphertext, and receive an encrypted prediction that only the user can unlock. The service never sees the input or the output. The CryptoNets work from Microsoft Research in 2016 demonstrated this end to end with a neural network. The limitations are real and well known: homomorphic schemes natively support only a restricted set of operations, mainly additions and multiplications, and computation grows slow and accumulates noise as it deepens, so models often have to be redesigned to fit and performance remains far below ordinary computation.
The technique sits alongside other privacy tools rather than replacing them. Differential privacy protects against what a result reveals; homomorphic encryption protects the data during processing. They address different threats and are sometimes combined.
For a business reader, homomorphic encryption is the answer to a specific question: can we use a third-party or cloud AI service on confidential data without that provider, or anyone who breaches it, ever being able to read the data. The honest caveat is cost. It is powerful and increasingly practical for narrow tasks, but still too slow for many large-scale uses, so it is best understood as a sharp tool for high-sensitivity, lower-volume work.