The general rule for evidence is that if it is relevant, it is admissible, unless it falls into a category of evidence that is excluded. Relevance here means that the evidence is something that will aid the court in determining the truth of any facts in dispute. Evidence that might be considered relevant, can be excluded if its value in assisting the Court, is outweighed by any prejudice that the evidence will create.
An example of evidence that is potentially relevant but excluded for its prejudicial effect is evidence of past convictions. A court's role is to determine what happened, and who was responsible, evidence of previous convictions could suggest that the defendant is capable of committing a crime, but the effect of the evidence would too often make the judge or jury (jury in particular) assume that the defendant was guilty, irrespective of the facts of the case. There are some limited exceptions to when a defendant can be cross-examined on their past convictions, generally surrounding where the defendant has made an issue of their good character.
Another evidence that is excluded for lack of relevance is the opinions of people who are not qualified to give expert opinion. The evidence is not relevant because it does not really matter what someone who is not an expert to give his opinion. Only people whom the court deems knowledgeable can make conclusions about the evidence tendered For example a prosecutor would not be allowed to ask a lay witness how long they thought a body had been dead for. The witness may be asked about the condition of that body when they found it. Then they may ask an expert in medical forensics to give evidence interpreting what the described condition would mean for the time of death.
Other evidence that may be relevant might be excluded for its unreliability. The classic case of this is hearsay evidence. What someone said to another about what happened is generally excluded because there is no way of cross-examining the person making the comment, and also the statement made may not reflect the reality of what happened. Although the hearsay evidence is often extremely relevant, it is excluded because it cannot be verified as being true.