Sentence fragment
Step-by-step explanation:
A sentence fragment fails to be a sentence because it cannot stand by itself. It does not contain even one independent clause.
After I finished packing my bags is a sentence fragment because it is a subordinate, or dependent, clause. It cannot stand by itself. It is a subordinate clause fragment. You need to attach an independent clause to make it a sentence. For example, "I left for the airport after I finished packing my bags." That would be a correct sentence.