Created in the hiatus of the original Captain Marvel after Fawcett Comics ceased publication in the 1950s, these comic book characters were created by Marvel partially to take advantage of the fact that the character name was available for copyrighting.
The first of these, Captain Marvel(I) was an alien Military Officer, Captain Mar-Vell of the Kree Imperial Militia, who had been sent to observe the planet Earth, which was of great interest to the Empire for its resource potential. Eventually, he realized the intentions of his superiors and rebelled, taking allegiance with Earth while the Kree Empire branded him a traitor.
Thence independent, the Captain fought to protect Earth from all menaces.
Later, he was punished with exile in the Negative Zone. The only way he could temporarily leave was to convince a young man, Rick Jones, to wear special metal wristbands called Negabands which allowed the two to switch places for a limited amount of time, much like the situation with the original Captain Marvel. Together, the pair continued the battle against evil.
Eventually Mar-Vell was freed and then became an appointed cosmic champion of space in general. However, this career was cut short because of an earlier incident when Captain Marvel stopped a villain from stealing a deadly nerve gas. In the case, he was exposed to it when its container leaked. While he seemed to have recovered after falling unconscious after successfully sealing the canister, the gas proved to be highly carcinogenic which eventually caused a fatal case of incurable cancer.
He died on Saturn's moon, Titan, in the presence of Marvel Universe's superhero community (as chronicled in Marvel's first regular graphic novel, The Death of Captain Marvel). The Negabands were eventually recovered and given to a hitherto unknown son of Mar-Vell.
A third Captain Marvel also exists in the Marvel Universe. He is the son of the first Captain Marvel.