The nitrification cycle is what occurs in your filter that actually "cleans" the water. Understanding this cycle is an important step in the care of any aquatic animal and will help you keep your water cleaner, filter it more efficiently, and also serve you well in case of a filtering emergency.
Start cycle: Ammonia
Now what is actually going on in your tank and filter is pretty interesting. We'll start from a new tank setup with only biological filtration (foam pads, ceramic rings, etc).
As your turtles, fish, etc. expel waste, it builds up in the water as ammonia. Initially there will be a pretty good spike in the ammonia level. 20% water changes every day or two should help keep that under control until your tank "cycles".
Ammonia to Nitrite
Aerobic bacteria are very little organisms. Just like us, they require oxygen and a "food source" for energy. In this case, the food source is ammonia.
As the ammonia rises, aerobic bacteria begin to colonize in the porous surfaces of the filter media where the water flowing through brings them more food (ammonia) and oxygen. Because of the plentiful food source (the spike in the ammonia levels) the bacteria population has a tendency to explode to the point of making the water cloudy. As the bacteria "eat" the ammonia, the ammonia levels drop and the bacteria expel waste. This waste is nitrite.
Nitrite to Nitrate
Now you will see a spike in the nitrites as the bacteria break the ammonia down into nitrites. It's now that the second type of aerobic bacteria take hold in the filter along side the first. These bacteria utilize the oxygen and nitrites in the water and produce nitrates. So now both your ammonia and nitrite levels will drop and should maintain at a nice low level. However, you will have a steady increase in the levels of nitrates.
Nitrates are less toxic than either nitrites or ammonia, so we can let them build up a little more. However, no aerobic bacteria utilize the nitrates as food. That's where the water changes come into play. The water changes are actually to reduce the nitrate levels. An interesting note is nitrates are good fertilizers. So high nitrate levels will promote algae and pond scum growth. At the same time live plants could help control nitrate levels a little but no turtle can resist tearing up all the plants. The waste water is great for gardens though or for growing your own aquatic plants in a separate tank.
Just because water has evaporated does not mean you don't need water changes! While water does evaporate, the nitrates stay in the tank. Regardless of the amount of water that is normally in the tank, you need to remove 20% of the current level, and then add water back in. Because of evaporation between water changes, you will always end up adding back in more water than you took out.
There are also devices called denitrators that can remove a certain amount of nitrates. Basically they work the same as the regular biological filtration except it's sealed and devoid of the oxygen that aerobic bacteria need. As a result, anaerobic bacteria take hold and use CO2 and nitrates from the water as food. They expel nitrogen and oxygen gas, and these gases escape into the air.
In the wild, nitrates are removed by plants and water flow. However, it is not possible to keep enough plants in a tank to control the nitrate levels produced by a turtle.