The conflicts in the play develop from an event that is revealed through exposition. During World War II, Joe Keller ordered his partner to conceal defects in 121 plane engines their company supplied to the Air Force during World War II. As a result, 21 fighter planes that were fitted with the defective parts crashed, killing those soldiers on board.
The significance of the title is made clear in the play's conclusion when Keller finally faces the truth of his own character and assumes responsibility for his actions. As a result of his greed and deception, he has lost the respect of his son Chris, a young man of principle. Keller's son Larry, who was shamed beyond endurance by his father's reprehensible acts, committed suicide. In addition to these sons, however, Keller finally takes direct responsibility for "all my sons," the soldiers who died flying the planes sent into combat with his defective parts. As the enormity of his selfishness and greed overwhelms him, Keller kills himself in the play's conclusion.
Joe Keller says that everything he has done in his life has been for his sons. This includes the decision to ship the cracked cylinder heads that lead to the death of so many airmen. Because Joe believes that nothing is more important than family, he has little trouble making this decision, although he does claim that he thought the heads would be discovered down the line and that he would be able to replace them with good ones with no harm to the business.
During the course of the play, pressed on by Chris' idealism, he comes to realize that the airmen who died because of his decision were not just strangers, men with no links to him; he comes to realize that they were "All My Sons," that you cannot act to favor your own sons to the harm of other sons. The realization of what he has done to these other sons leads to his decision to commit suicide.