Kripke’s term for an expression that has the same referent in every possibly world. This includes proper names and natural-kinds. Example:
“The 44th president of the United States” designates Barack Obama in the actual world, but it does not rigidly designate him because in some possible world John McCain is the 44th President of the United States. However, “Barack Obama” picks out the same essence in every possible world that “Barack Obama” designates anything at all.