Just explaining the things in the editor:
(To get to this page, open the editor, click Scenarios menu, then Custom Rules, say yes to the warning, then Rules -> Edit Rules, and the Difficulty Levels tab).
Cost Factor: How many shields it takes the AI to build a 10-shield project. On Chieftan it's 20, meaning it takes them twice as long to build something/research something, etc, than you. (Human cost factor is always 10.) On Monarch, it's 9, meaning projects are 9/10 of what they are for you (tech costs are lower too).
Max. Government Transition Time: Max number of turns it will have for anarchy. (0 means a normal anarchy). The higher the level, the less time the AI will spend in anarchy.
AI to AI trade rate: Simply, the higher the value, the more they'll trade between themselves. If this rate is 140, it'll treat an AI offer of 100 gold as 140 gold (but it'll actually receive 100). It gives cheaper discounts to other AIs.
# of Defensive / Offensive units: The number of units they get of each type. It will be all warriors unless an AI knows Bronze Working (Spearman for defense) or Warrior Code (Archers for offense) at the start of the game. Germany starts with no warriors, as it knows both those techs.
Number of start unit type 1 / 2: The number of ADDITIONAL starting units an AI gets. By default, they are settler for type 1, and worker for type 2 (you can change what the start unit type 1/2 are under the General Settings tab).
Num. of citizens born content: The number of citizens that will be content in your city before they start being unhappy and you need to use luxury tax/Military Police/luxuries, etc to quell them.
Num. citizens quelled by military: (1 for every difficulty level). Leave it at this, it means that one unit quells 1 citizen per turn in your cities.
Attack bonus vs. barbarians: This is a percent. On Chieftan you get 800% attack bonus meaning you and the AI have a way better chance against barbarians. A 3/3 Barbarian Warrior (1 attack) would be up against a 3/3 Human Warrior (treated like 8 attack!

).
Percentage of optimal cities: What percentage of the optimal city number on the World Sizes tab is actually the optimal number before heavy corruption.
Corruption: This is 100% on all levels. It means that corruption affects all cities normally as it current does in Civ3. Higher and you get less corruption, lower and you get more.
Hope this helps!
edit: Crosspost with denyd. He has a nice table showing it.