Nitrite (with an "i") is harmful and the reading should be zero.
Nitrate (with an "a") is less harmful in moderate amounts. A reading of 40 ppm or so in a tank is tolerable.
Both are byproducts of the breakdown of ammonia. Here's how it goes:
1. Turtle's pee ammonia. It is harmful and unhealthy. In an established healthy tank the test reading should be zero. What gets rid of ammonia is your bio-filter. The good bacteria in the bio filter convert the ammonia to......
2. Nitrite. It is also harmful. In an established healthy tank its reading should also be zero. What gets rid of the nitrite is also the bio filter. A second group of good bacteria in a bio filter convert nitrite to......
3. Nitrate. Not so harmful in moderate amounts. Good fertilizer for plants. If you don't have living plants in your tank and you don't change the water very often then the nitrates will build up and algae will thrive. You get rid of nitrates by changing the water and by keeping living plants in the tank (hard to do with hungry turtles around).
When a tank is new it takes time for the bacteria in a bio filter to adjust to the correct levels - usually several weeks (up to around 6 weeks). Until the levels reach equilibrium, the water turns cloudy white with bacteria. Also during this start up time readings of ammonia and nitrite are high and will fluctuate. Eventually however the levels of bacteria and chemicals level out and the water becomes crystal clear and the readings of ammonia and nitrite go to zero!
If however the tank is too small for the size of the turtle, or the filter is inadequate, or if there's overfeeding of the turtle, then the bio filter will never be able to handle the ammonia load properly and test results will fluctuate and there will be problems with odour and water clarity. The only alternative to fixing the size of the tank, the filter or the diet is to keep changing the water all the time. With a tank the right size, good filter and appropriate turtle diet the water does not need to be changed nearly so often.
Here's a thorough and more scientific explanation of the whole thing:
http://www.redearslider.com/water_quality_issues.html