The assertionMethod verification relationship is used to specify how the DID subject is expected to express claims, such as for the purposes of issuing a Verifiable Credential
The authentication verification relationship is used to specify how the DID subject is expected to be authenticated, for purposes such as logging into a website or engaging in any sort of challenge-response protocol.
The capabilityDelegation verification relationship is used to specify a mechanism that might be used by the DID subject to delegate a cryptographic capability to another party, such as delegating the authority to access a specific HTTP API to a subordinate.
The capabilityInvocation verification relationship is used to specify a verification method that might be used by the DID subject to invoke a cryptographic capability, such as the authorization to update the DID Document.
The keyAgreement verification relationship is used to specify how an entity can generate encryption material in order to transmit confidential information intended for the DID subject, such as for the purposes of establishing a secure communication channel with the recipient.
A verification relationship expresses the relationship between the DID subject and a verification method. Each flag corresponds to a bit, and the set of flags form a byte to represent the active verification relationships for a verification method.
See
https://www.w3.org/TR/did-core/#verification-relationships