The Marvel Family consisted of six individuals who had been granted special powers by the ancient wizard Shazam, and one fake. Shazam wielded his powers for 3000 years, before the rise of historic civilizations. Later, in Egypt he tried to give the powers to Teth Adam, known now as Black Adam, but this hero turned villain. Shazam decided to wait a while and, when his own death was imminent, to pass his powers on to children who were pure in heart.
So, when his time came, Shazam had a mysterious figure bring newsboy Billy Batson to him, and gave the lad mystic powers, which Billy gained by saying the wizard's name and changing into Captain Marvel, the World's Mightiest Mortal.
The next additions to the Marvel Family came when Billy, who was now working as a newscaster at station WHIZ, met 3 boys who shared his name; tall Billy Batson from Texas, Fat Billy Batson from Brooklyn and Hill Billy Batson from Nashville. These nicknames were chosen to differentiate them from the famous Billy.
Billy shared with the other boys his secret - that he was Captain Marvel. Even so, they were reluctant to speak the magic word, "Shazam."
Then Sivana entered the picture, with 3 evil associates; bandit "Biggy" Brix, Nazi agent Herr-Geyer, and the strange Captain Death. Each of these was sent by Sivana to capture Billy Batson - but they each captured one of his namesake's. The evil scientist sent a message to Billy to come in that identity or his friends would die.
Billy knew he was walking into a trap, but he took the chance - and the four boys ended up tied to a log in a sawmill, bound and gagged. Billy managed to get his gag off by holding his head just close enough to the saw. But the machinery was so loud, it drowned out his shouts. The other 3 Billies added their voices and the word was audible. All 4 became "Captain Marvels." But the others agreed there was only one Captain Marvel, so they became his 2nd Lieutenants - the Three Lieutenant Marvels.
After defeating the villains, the 3 other Billies agreed to speak the magic word only in concert with the first Billy. They first broke this agreement when Billy was framed for treason and they went to his assistance as the Lieutenant Marvels.
The next members of the family were Captain Marvel junior, Mary Marvel and Uncle Marvel. Mary Batson kept a diary of her work as Mary Marvel - her Good Deed ledger, as she called it. One day she lost it and it was found by a man named Dudley, who read it and thus learned the secrets of Mary, Billy and the rest of the Marvel Family. He then introduced himself to Mary as her long-lost Uncle Dudley from California. ("Everyone has an unknown uncle from California" he said). Moreover, when they both said, "Shazam" Dudley also changed - to uncle Marvel. (Although he simply shed his outer clothes to reveal a prepared costume beneath).
Dudley then set up a business, Shazam incorporated, with himself as president, explaining he would donate all proceeds of the Marvels' good work to needy causes and would make his enterprise a non-profit organisation. Mary soon realised that he was a fraud when he said, "Shazam!" without changing. But, being a good hearted soul, she let him continue with his pretense and the other Marvel Family members did the same.
Uncle Marvel often cried off when he was supposed to fly by claiming he had "Shazam-bago." Once he used an invention of his - a collapsible rocket motor - to fly, but it didn't work properly and it was soon abandoned. It seems Dudley is his last name, as he has a real niece named Mary Dudley (called Freckles). Although she sometimes wore a Mary Marvel costume and called herself Freckles Marvel, she never pretended to have Shazam powers an dis not regarded as a true member of the Marvel Family.
Another who has the Shazam powers is Hoppy the Marvel Bunny or Captain Marvel Bunny. He lives in a world of furry animals and is consequently not really part of the actual Marvel family. Though Kid Eternity is Captain Marvel Junior's brother, and as such he is a member of his natural family, he's not in fact a member of the super-power sharing Marvel Family.
At one time, the Marvel Family had a show on WHIZ-TV, and for several years they continued to fight all sorts of evil, until one day Sivana and his family struck at a ceremony honouring the Marvels. The heroes and their friends wound up in a globe of Suspendium for decades - an act which backfired on the Sivana's, for they too were trapped. Captain Marvel, Captain Marvel Jr. and Mary Marvel (and presumably everyone else) were freed by the events of the Crisis on Infinite Earths. All 3 continue to play major roles in the DCU - especially in the various crises that particular Universe/Multiverse is now facing.