The cycle of a tank is such:
Your fish eliminate into the water. This is ammonia.
The ammonia is broken down and recombined with oxygen by one type of bacteria that lives in your filter. The by-product of this bacteria - the re-combination of the ammonia - is nitrite.
The nitrite is then also broken down and recombined with oxygen by the second type of bacteria to produce yet another by-product - nitrate.
Real plants in a tank (including algae) can process this nitrate as a fertilizer to grow. In the absence of living plants, the nitrate levels can climb very high. To reduce the amount of nitrate in our tanks, we do a 20-30% water change at intervals determined by the amount of nitrate.
"Cycling" a tank simply means that you have given the two types of bacteria the opportunity to grow and colonize in your filter, gravel, and other surfaces of the tank, (The majority resides in the filter - for that is usually where there is far more surface area to colonize)and that there is now ample bacteria available to process the fish waste into the final product - nitrate.
Since you did not do a
nitrite test, what you are seeing is your cycle forming in the tank, but not seeing the "middle information. Typically the ammonia procesing bacteria kick in and start processing ammonia into nitrite. The second type of bacteria take a while to get going, but when they finally do, you will see them start processing the nitrite into nitrate. The fact that you are now seeing some nitrate means that the second type of bacteria are now up and growing in your filter and doing their job. As their colony grows and responds to the amount of waste your fish are producing, you should see zero ammonia, zero nitrite, and anywhere from 5-80-160ppm nitrate. When this happens you need to do a water change to bring the nitrate levels down to under 20ppm.
Good going - your tank is cycling!!!!