Hearsay evidence refers to statements made by a witness, which were based on what another person had told them and not on the witness' own observations or their own knowledge. Generally, hearsay evidence was disallowed in most courts or hearings, but some exceptions were made (e.g. administrative hearings).
Hearsay evidence was inadmissible under the Federation judicial system, but it was admissible under Tanugan law, if it came from someone who was deceased. Chief Investigator Krag noted this in 2366 when Jean-Luc Picard, who was holding an extradition hearing, initially objected to Krag's request to present hearsay testimony. (TNG: "A Matter of Perspective")