The character is named Balok (from the First Federation), and was first seen in the TOS episode "The Corobmite Maneuver".
The image is actually a fake, Balok's real appearence resemble that of a child.
Balok used the fake image to test if Kirk's claims of being friendly and looking for cooperation was truthful. He first attacked the Enterprise, then faked engine failure. When Kirk offered his assistance, rather than destroying Balok's disabled ship he knew the Enterprise were sincere in their claims.
There, you probably know more about the Kif image than you ever wanted to.