It means that you have nitrates in your source water and so in order to know that you've finished cycling your tank, you need to have a higher amount of nitrates than your source water's level ( assuming you are not using anything like plants or chemicals that absorb the nitrates or you are doing daily water changes.
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So let's assume that you have seen the spikes in Ammonia and Nitrites and at some point, they both went down to 0 ppm, you need to determine what is causing the ammonia level to rise now. What it may be is that you are getting a reading due to changing your water every day and since one of the products you were using is not removing it but just detoxifying it, what you are reading is NH4 ( ammonium) and not NH3 ammonia.
What I suggest is to stop doing daily water changes and test your water daily for the next week to see if the ammonia level continues to rise, fall or stay the same. A rise means that you do not have enough biological filtering to handle the ammonia production currently in the tank. ( be careful not to overfeed during this test period.) If it falls, it means you do.
You should also start seeing a rise in nitrates as well. If it stays the same, you need to check your reagents to make sure you are getting an accurate reading. Take a sample of your water to your LFS and have them check it with their kits and yours for comparison.
Keep in mind that while ammonia is not the best condition to have in a tank, Nitrites are worse for the fish
and so if the ammonia level is present but the nitrite level remains low or at 0, you should have a cycled tank. Remember the graph. If there is nitrite production, there is bacteria present. if there is nitrate production ( other than from your source water), there is the other bacteria present. Your job then is to not overload the system with fish and food.
Keep us posted