Definition from Nolo’s Plain-English Law Dictionary
At trial, an explanation to a judge by a party or the party's attorney as to how a proposed line of questioning, or a certain item of physical evidence, would be relevant to its case and admissible under the rules of evidence. Offers of proof arise when a party begins a line of questioning that the other side objects to as calling for irrelevant or inadmissible information. If the judge thinks that the questions might lead to proper evidence, the questioner will be give a chance to show how the expected answers will be both relevant and admissible. This explanation is usually presented out of the jurys hearing, but it does become part of the trial record.