Relevant evidence is evidence that is admissible in court based on the fact that it directly pertains to proving the case at hand. It is distinct from irrelevant evidence, which is inadmissible in a court of law since it serves no function. The question of what evidence is relevant depends on the case at hand.
Whether a civil or criminal case is being tried, there are generally several elements that go into determining the guilt or innocence of the defendant. For example, first degree murder is defined as the willful, malicious, premeditated and deliberate killing of a victim. Thus, in order for a prosecutor to prove that a defendant is guilty of premeditated murder, he must prove that the action was willful or intentional, that the defendant committed the killing to be malicious, that he planned it beforehand, that he committed the murder on purpose and that the victim was actually killed. If the prosecutor cannot prove malice, for example, or premeditation, the murder may be considered second degree murder instead.
Relevant evidence in such a case could be evidence that proves any element of the crime. For example, if the accused person had made threats against his mother's life a month before her death, those threats would be considered relevant evidence since they could go toward proving that the homicide was premeditated and malicious. On the other hand, if a person was on trial for bank fraud, the prosecutor generally could not introduce evidence that the defendant had made threats against his mother's life, since those threats would not be relevant to whether the defendant had committed bank fraud or not.
The determination of what is relevant thus depends on what the elements of the crime are. Relevance or lack of relevance is normally decided on a case-by-case basis. If one party believes the other is intending to present irrelevant evidence, he can make a motion to determine the "relevance" or object to the judge, requiring that the other party justify his presentation of the evidence and explain why it is relevant evidence.
When the relevance of evidence is challenged, the other party must then explain how that evidence helps him prove the theory of his case. For example, a defense attorney may wish to introduce evidence that the plaintiff's witness had cheated on a test. If the plaintiff's attorney objects and questions the relevance, the defense attorney could make an argument that the cheating was relevant evidence because it went toward the character of the witness and proved that the witness was a liar.