A forked tongue is a tongue split into two distinct ends at the tip. This is a feature common to many species of reptiles. Reptiles smell using the tip of their tongue, and a forked tongue allows them to tell which direction a smell is coming from.
The image has given rise to the expression "to speak with a forked tongue," meaning: to say one thing and mean another or, in more general terms, to act in a duplicitous manner. Early Western films represented it as a Native American saying with the (often hostile and evil) Indians uttering phrases like, "White man speak with forked tongue".