At trial, relevant evidence is admissible and irrelevant evidence is not. Something is relevant if it is tends to make a fact at issue in the trial more or less likely. This is not complicated. Information that would be useful in deciding the truth of the facts in dispute is relevant and admissible. And for good reason. An impartial jury wants to gather these facts in order to render a fair and just verdict.
So why would a litigant ever want to offer evidence that is not relevant? The simple answer is that a litigant offers irrelevant evidence at its peril. Focusing on the irrelevant can have the effect of aggravating the jury, or worse still, sending the message that you are purposefully attempting to distract it because you have the losing side on the relevant evidence. So as a general rule, keep it tight at trial. Be the litigant who is perceived as the one who values the jury’s time and is providing the information it needs to finish its job.