ELI5 : An Individual can prove the authenticity of a digital item without disclosing the details to insure privacy or prove they actually have the information without giving away information before a agreement or sale is made.

Some applications off the top of my head:

ZK-payment trustless* mixing without the need for third parties
Removing many required escrow agents from the sale of digital goods or information

More secure trustless* and verifiable auditing

Proof of registered assets or properties that can independently be audited(property titles) without disclosing details (location) that could compromise privacy

Smart contracts that can independently be audited for veracity but without disclosing the details therein for privacy



Example of use case from article--

"An example application would be the owners of a particular make of e-book reader cooperating to purchase the DRM master keys from a failing manufacturer, so that they could load their own documents on their readers after the vendor’s servers go offline. This type of sale is inherently irreversible, potentially crosses multiple jurisdictions, and involves parties whose financial stability is uncertain–meaning that both parties either take a great deal of risk or have to make difficult arrangement. Using a ZKCP avoids the significant transactional costs involved in a sale which can otherwise easily go wrong."

* Trustless within the constraints to a secure trust minimized block chain like bitcoin. Nothing is completely trustless.