It is so named because it can produce ripe fruit by July 4 (Independence Day in the USA) in the typical climate. Even in regions with the shortest growing seasons, the plant has been known to yield red tomatoes by early July.
Fourth of July was bred by Burpee, which maintains exclusive distribution rights. As with other hybrids, the variety’s parentage remains a well-guarded industry secret.

Gee, I thought all tomatoes were 4th of July tomatoes.