Civilization – the origin of the Qin Shi Huang theme music in Civilization IV

It's a matter of bonus and handicap. Some are for you and some for the AI.

Ref:

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.

There is a file that detail all those.

Coins are your money:

• You can trade them to other civilizations in exchange for anything: technologies, maps, resources, the other civilization going to war for you. (After researching the technology Currency)
• You can spend them to quickly finish new units and buildings. (depending on your civilization's current government)
• You can spend them to upgrade your units which have become obsolete into the newer better units. (But only inside your territory, or maybe even in cities, or in cities you have Barracks in. I can't recall which one sorry!)
• You spend them each turn to pay your units. If you're not earning enough coins each turn to pay your units, and you don't have enough in your treasury to cover the loss, your units will start disbanding. (Deleting themselves)
• You spend them each turn to pay for your cities to run. The more cities you have, and the further they are from your capital, the more they cost.
• You can effectively spend coins you've saved in your treasury on research, by setting your research high enough that you are losing coins. Just watch for your treasury running out!

I'm probably even forgetting a few. Just think of coin as money. What can you do with money? Spend it on things you have to, then spend it on anything you like if you have any left over!

If I've used any terms you're not familiar with, just ask for clarification in a comment.