In the U.S. military, G.I. originally stood for "Government Issue" (as in, equipment, rations, etc. that were provided by the government to the soldiers). Over time, it came to also describe soldiers themselves, who were called G.I.s (as in "G.I. Joe", "The G.I. Bill", etc.).
In biology and medicine, G.I. stands for "gastro-intestinal", referring to the digestive tract.