Enclaves are servers with special super powers.
They have very limited input and output abilities, so no one can connect into them easily. This can give you peace of mind. No beady eyes are looking at your data.
They also have the ability to request attestation documents signed by the underlying infrastructure. These are signed documents of the hashes of all of the source code and the environment running inside.
When a client connects to the enclave, this attestation document is shared through a secure handshake, authorising the user and validating that the enclave is doing what it is expected to do.
Payload encryption is maintained end-to-end meaning you don't have to trust the host of the enclave.
Oblivious makes it easy for you to deploy your servers to enclaves and for your clients to securely connect to them via a native client direct-proxy.