What is historical context in this example?

Historical context refers especially to the historic events that lead up to something or are, at least, related to it in some way.

Using the atomic bombs on Japan happened in context of the United States being several years into a long, difficult, costly war which began by being attacked by Japan. Those years of war overused and abused the American industrial and economic base to a point that could not long be sustained by 1945 while steadily and pervasively eroding quality of life in this country, even while it was technically winning the war, The US had suffered the deaths of 148,000 soldiers. And the world had lost over 20,000,000 civilians just from disease and starvation induced by the war.

At the time of the atomic bombing, Japan was militarily defeated but its imperial government refused lose face through surrender, propclaiming it would fight to the last citizen, and estimates were that at least another half million people would die and very significant portions of Japanese industry and cities would be destroyed over a period of many months or even multiple years trying to end the war through conventional fighting under those conditions.

Those facts form some of the historic context of the bombings.

To give the "historical context," you would describe the events in history that surround the bombing.

You would say that it was toward the end of WW II, that Truman took the advice of his military experts on how many Americans would be killed during an invasion of Japan, what was going on in the Japanese government at the time, etc.

You are not giving the "economic" situation surrounding the bombing, and you are not giving the "religious philosophy" context of this decision. You are also not reporting on the "cultural biases" context of this decision.

(But you could mention all of these if you think they are important historically to the topic.)

Instead, this assignment wants you to describe the historical factors that surrounded this decision.

("Context" means "the things that surround something.")