I would like to know what transaction fees are for, what they represent and how does one make money on these transactions?
Transactions fees are another incentive for miners to mine bitcoin. When you make a payment you segguest a fee for the miners to verify and approve it. A miner that verifies your payment recieves the fee.
So the way to make money from transactions fees is simply to be a bitcoin miner.
Today, new bitcoins are created as a reward for bitcoin miners. This reward gradually decreases and in the future the reward for mining will be solely from transaction fees, and the amount of bitcoin in the world will be constant at around 21 million.