The Great War is a catastrophic event that, although never shown, has been a reoccurring subject in the entire Salad Fingers series. As with most events and memories of Salad Fingers, it's unknown whether or not the war is a figment of his own imagination or an actual event that occurred.
Characters in the series that are known to have supposedly participated in the Great War are Kenneth (Salad Fingers' "brother") and Jeremy Fisher (one of Salad Fingers' puppets).
Background
No episode has ever given background to this event, but many fans speculate that the Great War is actually responsible for the almost lifeless post-apocalyptic world Salad Fingers and the rest of the characters live in.
In the 20th century, the only war referred to by this name was World War I (before World War II); the influence of this time period is reflected in Salad Fingers' behavior, manner of speaking, and such, as examined in Film Theory's two-part Salad Fingers series, which looked at various things throughout the series like locations, the trenches, Horace Horsecollar, "Over the Rainbow", and "We'll Meet Again" (both of which released in 1939, possibly ruling out the theory that the war being referred to is World War I. The most plausible, given this information, would be World War II, the Cold War, or a fictional war).
Another name for the war was 'The War to End All Wars'. If this name is true, then in this universe, the Great War did end all wars, and perhaps even civilization. Some believe that the series takes place after the Great War, around the mid-20th century, and some believe it takes place in a far-along, post-apocalyptic future.