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  A MAC algorithm is a family of cryptographic functions – parameterized by a symmetric key – that can be used to provide data origin authentication, as well as data integrity, by producing a MAC tag on arbitrary data (the message). In this Recommendation, an approved MAC algorithm is used for key-confirmation and may also be employed in certain key derivation methods.
Source(s):
NIST SP 800-56A Rev. 2 [Superseded]

  A family of cryptographic functions that is parameterized by a symmetric key. Each of the functions can act on input data (called a “message”) of variable length to produce an output value of a specified length. The output value is called the MAC of the input message. An approved MAC algorithm is expected to satisfy the following property (for each of its supported security levels): It must be computationally infeasible to determine the (as yet unseen) MAC of a message without knowledge of the key, even if one has already seen the results of using that key to compute the MAC's of other (different) messages. A MAC algorithm can be used to provide data-origon authenication and data-integrity protection. In this Recommendaton, a MAC algorithm is used for key confirmation; the use of MAC algorithms for key derivation is addressed in SP 800-56C.
Source(s):
NIST SP 800-56B Rev. 2

  A family of one-way cryptographic functions that is parameterized by a symmetric key. A given function in the family produces a MacTag on input data of arbitrary length. A MAC algorithm can be used to provide data-origin authentication, as well as data integrity. In this Recommendation, a MAC algorithm is used for key confirmation and key derivation.
Source(s):
NIST SP 800-56B Rev. 1 [Superseded]