Broadly, an out-of-court statement offered to prove the truth of whatever it asserts. Hearsay evidence is often inadmissible at trial. However, many exclusions and exceptions exist. Evidence meeting the broad definition may not actually be hearsay under the court's evidence rules. Even hearsay may be admitted if exceptions are met.
Generally, an out-of-court statement is hearsay if the parties care about whether or not the statement is true. For the purposes of the rule, it does not matter whether the statement was oral or written. Generally speaking, hearsay cannot be used as evidence at trial.
For example, suppose that a witness stopped at the scene of a car crash. At the crash site, an injured driver stumbled up to her and said "Martians caused the accident!" Because of the hearsay rule, the statement cannot be used as evidence that Martians caused the accident. It could, however, be used as evidence that the injured driver was capable of speech after the crash. The rule would also bar the testimony if the injured driver scribbled his message on a scrap of paper and handed it to the witness.
In general, the hearsay rule is motivated by a belief that hearsay is unreliable. There are exceptions to the rule for for particularly reliable statements, and where allowing the evidence advances public policy goals. For example, under Rule 801(d) of the Federal Rules of Evidence, a witness's prior inconsistent statements are not hearsay, due to the public policy goal of avoiding perjury. Similarly, Rule 803(6) of the Federal Rules of Evidence makes an exception to the hearsay rule for business records, because businesses have incentives to keep accurate records.
Although hearsay rules differ by jurisdiction, many state hearsay rules are modeled on the Federal Rules of Evidence, which contains about 30 exceptions and exclusions to the hearsay rule. See state civil procedure rules; Federal Rules of Evidence.
See Civil Procedure, Evidence. For more on some hearsay exceptions, see Forfeiture by wrongdoing, Present sense impression, Declaration against interest, Dying declaration, Excited utterance, Past Recollection Recorded, business record exception, and former testimony exception.