Proxy re-encryption (PRE) is a form of public key encryption that allows a semi-trusted proxy to transform ciphertext from being encrypted under one key to another, without learning anything about the underlying plaintext. A "re-encryption key" is used by the proxy to do this transformation.

Umbral is a split-key version of PRE, which splits the re-encryption key into many shares. A threshold number of these shares are then required to re-encrypt the data (similar to Shamir’s Secret Sharing).

Here's a post describing split-key threshold proxy re-encryption in slightly more detail: https://blog.nucypher.com/unveiling-umbral-3d9d4423cd71