An evidentiary hearing is a hearing initiated by a court that takes place when the court is about to make a legal decision. This can occur in the context of, for example, an appeal.
The court can decide to hold an evidentiary hearing on the entire appeal, or just a portion of it. For example, if an appeal alleges to claim three new pieces of evidence, presents one affidavit of an eye-witness, and one affidavit of a scientist, the court could decide to hold an evidentiary hearing on the affidavit of the eye-witness while the rest of the appeal is dismissed.
At the evidentiary hearing both sides may question the eye-witness and may also present their own evidence and witnesses.