Can anyone explain what are the differences (like attacking style, culture development, etc) of the enemies in Civilization IV between the various difficulty levels?
It's a matter of bonus and handicap. Some are for you and some for the AI.
Chieften, Settler, Warlord... they all give bonuses to the human, or handicap the AI in one manner or another... these lower levels are easiest for the human and hard on the AI.
At Noble, both sides are at their closest parity in regards to breaks to either side... Prince through Diety all favor the AI with increasing bonuses and gameplay ease, making it harder on the human.