The term "smoking gun" is a reference to an object or fact that serves as conclusive evidence of a crime or similar act, just short of being caught in flagrante delicto. Its name originally came from the idea of finding a smoking (i.e., very recently fired) gun on the person of a suspect wanted for shooting someone, which in that situation would be nearly unshakable proof of having committed the crime. The phrase originated in the Sherlock Holmes story, "The Adventure of the Gloria Scott" (1893).
In addition to this, its meaning has evolved in uses completely unrelated to criminal activity: for example, scientific evidence that is highly suggestive in favor of a particular hypothesis is sometimes called smoking gun evidence. A piece of evidence that falls just short of being conclusive is sometimes referred to as a "smoldering gun."