Say you need to make financial inferences based on confidential financial reports. However, the nice deep learning model you want to use resides on a remote server you do not trust. Then how can you query the server but still ensure that the confidentiality of your data is still intact? Fortunately, there are a couple of ways to handle this problem. Homomorphic Encryption (HE) is one of these methods.
In a nutshell, HE allows you to perform computation on encrypted data. Referring to the inference problem above, you can encrypt your data, get the inference done on the server without decrypting it, and finally decrypt the output to get the inference. However, this ultimate level of flexibility comes at some cost. HE is not computationally efficient yet. There have been continuous efforts to improve its performance with some remarkable results in recent past. But, at least for machine learning applications, there is a long way to go.