Hydra ZK Proving Schemes
The Hydra family bundles proving schemes that use Hydra Delegated Proof of Ownership.
The following article from Vitalik Buterin should give you a precise understanding about the intent behind Hydra and a general overview of the ZK SNARK concepts behind it.

Hydra Proving Scheme Family

The Hydra Family currently has three proving scheme members. A Proving Scheme has a prover that is able to generate proofs for a verifier that can verify their validity.
  • Hydra-S1 Proving Scheme (circuits, docs) (S1 Single Source. Version 1: one group membership verification) Two attesters have implemented Hydra-S1 Proving Scheme to generate ZK Attestations:
  • Hydra-S2 Proving Scheme (S2: Single Source. Version 2: multiple membership verifications) Open-sourcing soon
  • Hydra-M1 Proving Scheme (M1: Multi Source. Version 1) Open-sourcing soon

Hydra Proof Of Ownership

In order to use Hydra proving schemes, the user must interact with a trusted Commitment Mapper from their account, and commit the Poseidon hash of a secret to receive the EdDSA signed receipt (mapping their account with their commitment) from the commitment mapper.
The user secret and the commitment mapper's signed receipt form the Hydra Proof Of Ownership
The user will then be able to use its Hydra Proof of Ownership in a SNARK to prove ownership of its account.
Using the commitment mapper with the Poseidon Hash function and the EdDSA signature schemes makes the Delegated Proof of Ownership cheaply verifiable in a SNARK.
All Hydra Proving schemes use one or multiple Hydra Proof of Ownership verifications.