GI is short for "Government Issue", a descriptive term for supplies distributed by the government. Originally it referred to "galvanized iron", the same material used in military supplies like trash cans & buckets. "GI" was stamped on these items - meaning they were made of galvanized iron.

Later the definition of GI broadened and during World War I it was used to refer to all things Army-related. This led to the reinterpretation of the term as "government issue".

The prevalence of the term led soldiers in World War II to start referring to themselves as GIs. Some servicemen used it as a sarcastic reference symbolizing their belief that they were just mass-produced products of the government. This has never been truer than it is today.

In 1944, the famous bill signed by President Franklin Roosevelt, the Servicemen’s Readjustment Act, which provided a range of benefits for returning World War II veterans, became commonly known as the GI Bill. GI Joe also became a term for U.S. soldiers when cartoonist Dave Breger, who was drafted into the Army in 1941, coined the name with his comic strip titled “G.I. Joe”.

More Info: en.wikipedia.org