Fundamental analysis is a way of understanding the market looking at the economic, political and social forces that drive supply and demand. In other words, you look at which country's economy is doing well and which country's economy is doing bad. The idea behind this type of analysis is that if the economy is doing well, then its currency will be strong because the better the economy of a country, the more confidence in its currency other countries have.
For example, the euro is gaining ground since the economies of the Eurozone countries are gaining ground. Fundamental analysts think as follows: As the business climate improves, the ECB (European Central Bank) will raise interest rates to control inflation and as a result the euro will continue to head up. So I will buy euros.
There are certain economic news that greatly impact greatly the currency market, e.g. NFP or Non-Farm Payroll (that is, US job rate excluding jobs in agriculture). But will get to this subject later.