EarthForce is the Space Division of the Earth Alliance
Presumably, it was founded upon the Discovery of an Extraterrestrial race, the Centauri Republic and needed as a requirement for the defense of Earth.
If this is true, EarthForce was in full effect in the Dilgar War and made some of it's first major victories there. This earned both reputation and the respect from the Centarui, the Narn Regime, and the League of Non-Aligned Worlds, making the Earth Alliance one of the big players in this section of the Galaxy.
EarthForce was defiantly in full effect during the entire Earth-Minbari War, in which it suffered many defeats at the hands of the Minbari Federation. Earth Force and the Earth Alliance would have been slaughtered if the Minbari Grey Council had not ceased all hostilities at the very brink of Earth's Atmosphere, at The Battle of the Line.
In the Babylon 5 Universe, the EarthForce military has the most disposable funds of all the races (aside from the Vorlon Empire), and the heartiest military force in the neighborhood.
The Omega Class Destroyers are the mainstay of the fleet, and through technologically inferior to some of the other major races, the sheer numbers makes the Earth Force quite a foe.
In 2261 the Earth Alliance fell into Civil War, and in 2262 many EarthForce vessels staged a military coup on President Clark, this pitted EarthForce against EarthForce until Sheridan and his attack force (a fleet made up of the Army of Light and EarthForce renegades) liberated Earth from Clark's order of martial law.
It is not clear, in the Babylon 5 history if EarthForce is ever replaced. It is presumed that the EarthForce takes part in the Telepath War, years after the Earth Civil War, and exists through the following decades.
In 2762 Earth falls into another Civil War, it is uncertain if EarthForce, or the Earth Alliance are still in operation, however, it is very certain that neither organization, or any Earth Organization from before this event, survives the Great Burn which is Earth's defeat in this conflict.
However, the human race does survive.