A World War II effort in the US, with the cooperation of the UK, to develop the first atomic bomb, directed by American physicist Robert Oppenheimer. A similar effort was undertaken in the USSR headed by Kurchatov. Token efforts in Germany, headed by Werner Heisenberg, and in Japan, were also undertaken.
With the cryptology and cryptographic efforts centered at Bletchley Park and the development of radar at MIT's Radiation Lab, the Manhattan Project represents one of few massive, secret, and outstandingly successful technological efforts spawned by the conflict of World War II.
Richard Rhodes' books about the development of atomic weapons, The Making of the Atomic Bomb and Dark Sun: The Making of the Hydrogen Bomb point out the immense scope of the bomb producing effort--the industrial effort that produced the first bombs was on a scale comparable to that of the entire US automobile industry at the time.
The industrial problem was centered around the production of sufficient fissionable material, of sufficient purity. This effort was two-fold, and is represented in the two bombs that were dropped.
The Hiroshima bomb was uranium-235, a minor isotope of uranium that has to be physically separated from more prevalent uranium-238, which is not suitable for use in an explosive device. The separation was effected mostly by gaseous diffusion of uranium hexachloride, but also by other techniques. The bulk of this separation work was done at Oak Ridge.
The Nagasaki bomb, in contrast, consisted primarily of plutonium-239, a synthetic element which could be induced to critical mass only by implosion. The design of an imposion device was at the center of the efforts by physicists at Los Alamos during the Project. The property of uranium-238 which makes it less suitable directly for use in an atomic bomb is used in the production of plutonium--with sufficiently slow neutrons, uranium-238 will absorb neutrons and transmute into plutonium-239. The production and purification of plutonium was at the center of wartime, and post-war, efforts at Hanford, using techniques developed in part by Glenn Seaborg.