Glossary
Hearsay
A statement made out of court, offered as evidence to prove the truth of what was said. Hearsay is generally not admissible: though there are dozens of exceptions and exclusions.
The classic example: "My friend told me the light was red." The witness saying that can't testify to it as proof the light was actually red: that's hearsay. The friend would have to come testify themselves.
The reason for the rule: out-of-court statements weren't made under oath, the original speaker can't be cross-examined, and the jury can't see them to evaluate credibility. So secondhand reports are presumed unreliable.
The exceptions are extensive: excited utterances made during a stressful event, business records kept in the regular course of business, statements made to doctors for treatment, dying declarations, and many others. The hearsay rule is one of the most technical areas of evidence law.