To exculpate means to find someone not guilty of criminal charges. If you've been wrongly accused of robbery, you'd better hope a judge will exculpate you, unless you want to go to jail because you've heard prison food is amazing.
Exculpate comes from two Latin words: ex-, meaning "from," and culpa, meaning "blame." Exculpate is similar in meaning to exonerate. When you exonerate someone, you clear a person of an accusation and any suspicion that goes along with it. Exculpate usually refers more directly to clearing the charges against someone. So if that judge exculpates you from the robbery charge, everyone in town might still think you did it. Get him to exculpate and exonerate you.