To testify typically refers to giving oral testimony under oath at a trial or possibly at a deposition.
To make a declaration of truth or fact under oath; submit testimony.
To make a solemn declaration under oath or affirmation for the purpose of establishing a fact: give testimony: to declare in testimony.
Lect Law Library
To give evidence according to law; the examination of a witness who declares his knowledge of facts.
The Free (Legal) Dictionary
v. to give oral evidence under oath in answer to questions posed by attorneys either at trial or at a deposition (testimony under oath outside of court), with the opportunity for opposing attorneys to cross-examine the witness in regard to answers given.
In the law, testimony is a form of evidence that is obtained from a witness who makes a solemn statement or declaration of fact. Testimony may be oral or written, and it is usually made by oath or affirmation under penalty of perjury. Unless a witness is testifying as an expert witness, testimony in the form of opinions or inferences is generally limited to those opinions or inferences that are rationally based on the perceptions of the witness and are helpful to a clear understanding of the witness' testimony.