Before World War II, the United States had never had a formal intelligence agency. The task of gathering and processing intelligence had been split between many different entites. At the end of the war, President Truman dissolved the OSS, thinking that the US could go back to the way things had been.
However, with the Cold War coming on, this was clearly not feasible. It was clear that the US would need one agency to be in charge of all intelligence so that the process of gathering and analyzing the intelligence could be made as efficient as possible. It was due to this that the CIA was created. It was given powers that the OSS had never had. It became the major agency that was responsible for all intelligence work.
The CIA succeeded the OSS, then, because there was a need for a centralized intelligence system and because the OSS had not had the powers needed to play such a role.