Do you mean physically -- the actual effects of the bombs themselves -- or socially -- the psychological/sociological/political effects of the bombing on the Japanese people?
Physically, the cities of Hiroshima and Nagasaki were subjected to enormous destruction. Although inefficient by modern standards, the atomic bombs used in Japan were more powerful than any conventional explosive, and caused incredible devastation across the city in the form of explosive damage, enormous stress damage from winds, and long-term radioactivity. The two cities suffered casualties between 150,000 to 300,000 by the end of the year, with many dying from radiation exposure. Although the damage was extensive and the area dangerous for years, today both cities have been largely rebuilt and are major population centers.
Psychologically, the effects of the bomb was to undermine Japanese feelings of military power. During the war years, Japan had successfully fought alongside Germany and created a sense of nationalistic pride. The attack on Pearl Harbor served much the same purpose, undermining the U.S. sense of superiority. With the atomic bombings, it became clear that not only was there a new and terrible weapon available, but that the U.S. was not afraid to use it as a military weapon. Emperor Hirohito famously stated:
"Should we continue to fight, not only would it result in an ultimate collapse and obliteration of the Japanese nation, but also it would lead to the total extinction of human civilization."
(Hirohito, Capitulation Announcement, Wikipedia)
After these events, the people of Japan were demoralized both economically and militarily for a long time. In later years, Japan became a center of manufacturing and technological progress, regrowing their economy through international trade.