It signs the transaction (eg. initiated by an application user, with an associated blockchain identity, issued by his/her org) with its private key and includes its public key in the transaction payload sent to peers and/or orderers. Peers and orderers (part of the Fabric blockchain network) then verify the signatures using the public key in the transaction. A state/credential store would be used to store the public certificates for enrolled identities that the application needs to use, whereas the crypto store would be used to store the private keys of identities and there are different types of stores available when using the client SDK