cycling is nothing more than bacterial colonies establishing themselves in your aquarium.
there are two types of bacterial colonies that are needed in any aquarium and they each play a role in breaking down wastes. respiration in fish, excess food breaking down, and fish waste all produce ammonia.
this ammonia is highly toxic to fish. in an established aquarium, the first group of bacteria convert ammonia into nitrite. nitrite is not as harmful to fish, but it is still nowhere near a good thing. this is where that other group of bacteria come in. their job is to break down nitrite into nitrate. an aquarium which has a healthy colony of both bacteria types is said to be cycled. this aquarium will have a zero reading for both ammonia and nitrite. nitrate readings in an aquarium that has just completed cycling will typically be off the chart high, and water changes will need to be made to bring this level down. most aquarists that i know try to keep nitrate levels as low as possible, but i believe that it wont be toxic under 80ppm.(someone correct me if i am wrong. PLEASE)
now. all that being said, it sounds like your tank isnt done cycling yet. if you have fish in this tank, i would suggest trying to find someone else to take them till your tank is cycled, or returning them to the fish shop, or doing frequent water changes to protect your fish. if you dont have fish in the tank, then i would suggest reading the pinned article at the top of the forum about fishless cycling and taking that advice. thats the method i am using as we speak.
whatever you decide, i hope all goes well. good luck and happy fishkeeping!!
