To proffer is to bring forth something to be accepted or rejected. In the context of the law, proffer most commonly refers to things that are presented as evidence in a trial to be used to support a position. Once proffered, the evidence can be accepted or rejected by the judge, based on its legality and relevance.
Even if evidence that is proffered at a trial has a high degree of relevance to the case, it can still be rejected by the judge if it was illegally gathered. For example, if a lawyer or law enforcement members searched a home without a warrant, any evidence they found inside could be dismissed. Also, if law enforcement got a statement from an arrested person without reciting the Miranda warning to him or her, then this evidence too could be dismissed by a judge.