In the blockchain space, an oracle is a party which relays information between smart contracts and external data sources. It essentially acts as a data carrier between smart contracts on the blockchain and external data sources off the blockchain. So one approach to keeping information “private” is simply to use oracles to fetch private information from an external data source.
What you can’t achieve with SNARKs on Ethereum, however, is autonomous privacy, separate from a user. Since SNARKs on Ethereum rely on a user to maintain the secret off-chain, without that user, there’s nowhere to keep track of the secret.