Acknowledged before or to me

What does Acknowledged before or to me mean in American Law?

The definition of Acknowledged before or to me in the law of the United States, as defined by the lexicographer Arthur Leff in his legal dictionary is:

Language which almost always appears in the certificate of acknowledgment of the person or persons in whose presence a formal acknowledgment is made, testifying that the acknowledging party’s act was made in the physical presence of the person certifying it.