OP_CHECKDATASIG and OP_CHECKDATASIGVERIFY check whether a signature is valid with respect to a message and and a public key. The message is restricted to exactly 256 bits, if longer messages are to be signed, it is recommended to sign the messages hash.
OP_CHECKDATASIG permits data to be imported into a script, and have its validity checked against some signing authority such as an "Oracle".
OP_CHECKDATASIG and OP_CHECKDATASIGVERIFY are designed to be implemented similarly to OP_CHECKSIG [1]. Conceptually, one could imagine OP_CHECKSIG functionality being replaced by OP_CHECKDATASIG, along with a separate Op Code to create a hash from the transaction based on the SigHash algorithm.