I think jay0705 has the sequence reversed a bit. Ammonia is converted to nitrite in the presence of oxygen, and the resulting nitrite is then converted to nitrate. Finally, in the presence of very low oxygen (as might be found in the crevasses of live rock) the nitrate is converted into nitrogen gas, which is vented off. This last step is very slow, so normally there will be a gradual accumulation of nitrates in the water. In a cycled tank there should be no ammonia or nitrite detectable, but nitrates are commonly measurable (depending on the set up). If you are planning a FOWLR, then some nitrate is OK (fish tolerate nitrate, just not a lot), but if a reef tank is your goal then you will have to get rid of the nitrate by water changes, or through biological means (macro algae, algae scrubber) or a reactor, all coupled with careful feeding.