The "peace symbol" of a circle with a vertical line all the way across and two lines from the center to the edge at approximately the positions of 4 o'clock and 8 o'clock (that's ☮) was designed in 1958 by English designer Gerald Holtom. Holtom wanted a simple symbol to be carried by people during a march from London to Aldermaston by the British organization Direct Action Committee Against Nuclear War. (The newly named Campaign for Nuclear Disarmament found the idea of a protest march to be too radical at the time.) Holtom had first thought of a Christian cross, assuming that churches would support the idea of peace, and also because the march was to start on Good Friday and end on Easter Monday. However, as Holtom said later, "all the church leaders who I interviewed refused point-blank to associate their religions with the March project."
Holtom then decided to make a new symbol. In one interview he described the lines in the circle as meant "to mean a human being in despair"; in others he said that the lines came from the semaphore signs for "N" and "D" for "nuclear disarmament." The organizers of the march were at first skeptical, but accepted the design and Holtom's advice for making "lollypops" with the symbol for marchers to carry. Hugh Brock, one of the organizers, recalled that "He insisted the symbols be mounted on very light laths of wood so that the marchers could carry them easily on the physically exhausting march, and more importantly, that they be pasted on to light card with waterproof adhesive to withstand bad weather." The symbols were painted in white on a black background, many by Holtom and his teenage daughter Anna in his Twickenham workshop. He said in 1961 that he'd originally "intended the lollypops to be stuck into the ground on their wood laths at stopping places so that they would appear like a Field of Remembrance in which a great family picnic was taking place. It never quite happened like that, but it might do yet."
While not all of the ideas for use of the symbol happened as Holtom envisioned, the march was a great success, with 10,000 people at the end outside the Aldermaston atomic weapons research plant (though only 500 or so people actually walked the entire 52 miles). And the symbol took off as well. The Council for Nuclear Disarmament took over the march the next year, and ceramic artist Eric Austin made pin-on badges with a peace symbol on them, distributed with the attached message, "In the event of a nuclear war, these fired pottery badges would be among the few human artifacts to survive the nuclear inferno." By 1961, the more civil-disobedience-oriented British organization Committee of 100 Against Nuclear War also used Holtom's symbol on its banners; the American Committee for Nonviolent Action used the symbol in 1960 while protesting the launching of Polaris submarines armed with nuclear missiles and the following year in its San Francisco to Moscow Walk for Peace, exposing people in the Soviet Union to the symbol.
The American anti-nuclear group Women Strike for Peace superimposed the peace symbol on a U.S. flag in 1962; by 1965, high school and middle school students in Des Moines, Iowa were suspended for wearing armbands with the peace symbol on them, one of the first uses of the symbol to specifically protest the Vietnam War. In 1971, Peggy Duff, general secretary of the CND, wrote of the symbol that "I have found it all over the world, on Glasgow bus shelters, on tiny villages in East Anglia and the Isle of Wight, far afield in the United States, in Greece, in Japan." The government of South Africa tried to ban the symbol in 1973 due to its use by anti-apartheid groups. Environmental organizations such as Greenpeace used the symbol, along with many other groups. Neither Holtom or the CND ever tried to copyright the design, and the U.S. Patent and Trademark Office's rejection of two different companies' attempts to trademark the symbol in 1970 officially put it in the public domain.
By the end of the 1960s, the symbol was strongly associated in the United States with anti-Vietnam protests and the youth hippie culture; this is probably why rumors spread about its origins. The John Birch Society magazine American Opinion claimed in June 1970 that the symbol was a "broken cross" carried by Moors invading Spain in the Middle Ages, or representing the upside-down crucifixion of St. Peter. (The Alternative Religions page at About.com notes that, "It is a common conceit in some evangelical Christian circles to refer to the symbol as anti-christian, and they refer to it as a 'broken cross' or 'Nero's cross,' referring back to the story of the upside-down crucifixion, supposedly at the hands of Emperor Nero. Thus, it is supposed to be a Satanic emblem -- somehow, Satanists at the beginning of Christianity are supposed to have adopted the emblem of a Saint to somehow signify the defeat of Christianity. It makes no sense, but little in these convoluted conspiracy theories ever does.") Others have said that it was a "witch's foot" or "crow's foot," some kind of medieval icon of the Devil; that it was a symbol used by the Nazis; or that it was an ancient Nordic rune meaning death. Certainly, none of these meanings were in Haltom's mind when he came up with the symbol.
Holtom eventually changed his mind about his original association of the symbol with "despair," and turned the symbol upside down, so that the diagonal lines did not droop but went upward. In this version, the diagonal lines symbolized the semaphore letter "U," for "unilateral disarmament." This version does not seem to have caught on, but it's the version of the symbol that Holtom requested be carved on his gravestone. He died in 1985 at the age of 71, but the peace signs carved on either side of his name on the gravestone are the standard kind rather than the inverted ones.
Sources:
Kolsbun, Ken, and Michael S. Sweeney. Peace: The Biography of a Symbol. Washington, D.C.: National Geographic, 2008. (book's site at http://peacesymbol.com/)
http://www.happybirthdaypeace.com/1194959839.cms
http://news.bbc.co.uk/2/hi/uk_news/magazine/7292252.stm