That's the one... the story is much more involved than even what Wiki mentions, but that is essentially it.
I think a key line here would be:
"Operation Ajax was the first time the Central Intelligence Agency was involved in a plot to overthrow a democratically-elected government."
The CIA was just 6 years old at the time, and what did they put in the place of the democratically elected official? A dictator of their choosing, forever ensuring that 5 US companies would control the majority of the oil in Iran and the people of Iran would control exactly 0%.
How was this done? Primarily through inciting riots and feeding false stories to the media. The people turned on themselves... and to this day, there are many who still feel very upset about this time in history.