Meacham told CBS News Early Show Co-Anchor Jane Clayson that the movement is in danger of slipping into myth.
"When we look at the stirring footage and celebrate Dr. King's birthday, right now, the movement increasingly seems like a far-away story," said Meacham. In fact, "we didn't know what was going to happen. If you act as though you knew it was all going to have a happy ending, you can't really appreciate the extraordinary sacrifice of the countless brave souls who led the way," said Meacham.
The book has essays from Maya Angelou, E.B. White, John Steinbeck.
Meacham said the great task in deciding which essays to include in the book was to find stories that would surprise people.
One story was written by Congressman John Lewis from Atlanta, "a man who still bears the scars of physical bravery in public life," explained Meacham. He read an excerpt from Lewis' account of Bloody Sunday, a non-violent march across a bridge in Selma, Alabama, almost 35 years ago. Lewis was beaten by a large, husky trooper.
"Without a word, he swung his club against the left side of my head. I didn't feel any pain, just the thud of the blow and my legs giving way. I raised an arm, a reflex motion, as I curled up in the prayer for protection position. And then the same trooper hit me again, and everything started to spin. If there was ever a time in my life for me to panic, it should have been then but I didn't. I remember how strangely calm I felt as I thought, 'This is it. People are going to die here. I'm going to die here.'"
Meacham chose Lewis' essay because it shows that "In the middle of America in the middle of the century, you had people running a prevailing white-run order." The civil rights protesters had "no earthly idea of whether they would make it through the day, much less change a nation's habit of heart and mind."
"The power of narrative is the single most powerful thing we've got," said Meacham. "I think it's so important to explain that John Lewis was a college kid in Nashville," when he started demonstrating at segregated lunch counters.
"These were incredibly young men People like you and me, if we were blessed with that kind of moral courage, might be able to do something like this. Then I think kids begin to connect to that and realize they too, could make a difference."
Meacham adds that it's important not to turn Dr. King into merely a mythological figure.
"King is a human -- he's a very human leader," said Meacha. "If we let him slip off and become someone we commemorate once a year and have department store sales about him, and people don't go to school, we're at risk of losing his humanity Heroes only work really when you realize you could have done that, too, given the opportunity for greatness."
Meacham's views on civil rights were influenced by his experiences growing up in the South.
"I grew up in the Civil War battlefield, in Mission Ridge, Tennessee," Meacham explains. "When I was 10 years old, I remember riots in Chattanooga, Tennessee, after some klansmen were acquitted in a shooting. If someone my age, just over 30, can see the echoes, the horrible echoes of Jim Crow, it's right there."
"I hope the book brings the struggle alive because, God knows, it is still going on," said Meacham.
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