Short Answer:
Gibson electric guitars date all the way back to 1894 with founder Orville Gibson. Gibson's original market, mandolins, gave way to electric instruments after the turn of the century before eventually evolving into the electric guitar market we know today from contributions from figures like CEO Ted McCarty and musician Les Paul.
Long Answer:
The Gibson story begins with Orville Gibson right before the turn of the twentieth century. His main market, propelled by his patented single-piece mandolin, gave way to a new electric instrument market brought on by America's new musical fascinations. Gibson experienced success up until the Second World War due to shortages of woods and metals, though they pushed through into post-war prosperity under the direction of CEO Ted McCarty. McCarty's artistic lens propelled the Gibson corporation into a new frame of success.
Throughout the '50s into the '60s, Gibson embarked on a new journey of artistry as new collaborations with rising musical stars such as Les Paul resulted in groundbreaking, new innovations in electric guitar design. The Gibson Les Paul, among the many innovative electric guitar models produced by Gibson, became an icon in its own right throughout the '50s, '60s, and '70s. Further innovations brought the Gibson SG ("solid guitar"), Gibson Explorer, Gibson Flying V, and Gibson Firebird, among many others.