Argo is taken largely from a book about the storming of the US Embassy in Iran in 1979, when a lot of American staff were taken hostage. This event certainly happened and was a very major incident at the time - it was probably one of the main reasons why the US President of the day, Jimmy Carter, lost the next election to Ronald Reagan as it made him look weak.
The book that helped to inspire Argo, Master of Disguise, was written by a former CIA operative named Tony Mendez who was involved in the secret operation that led to the eventual rescue of the hostages, when CIA operatives pretending to be Canadians gained entrance to the embassy.
So the film has a definite factual basis. However, it has implied that the CIA managed the rescue almost single handed, whereas in fact they needed a lot of help from the Canadian government. There are a number of other inaccuracies, but the film does have a histhorical basis.