Civil Litigation-Relevance
The principle criteria of admissibility is that the evidence must be relevant. Relevance means that the evidence that is being offered tends to prove or disprove an issue in the case. If the issue in the case is whether you ran a red light, evidence that shows that the traffic light was not properly functioning at the time of the accident is relevant and typically would be admissible. Likewise, evidence of the cycle of nearby traffic lights and your speed as you traveled from a nearby intersection to the intersection in question may all be relevant to whether or not the light was red when you entered the intersection. All of those facts tend to prove or disprove whether you ran that red light and therefore are relevant.
Relevance means that the evidence that is being offered tends to prove or disprove an issue in the case.
Some evidence may be relevant but it is so highly prejudicial that the court determines that it should not be admitted. In tort claims, most courts have determined that evidence of insurance is not admissible because it is too prejudicial. If a jury knew that a defendant was insured, then jury verdicts may be higher simply because of that. Accordingly, most courts have determined that evidence of a defendant being insured is not admissible even though it may be relevant.