Ammonia is a chemical found in windex and whatnot. It is a nitrogenous waste that fish get rid of by means of a form of urine through their gills, and it is also found in fecal matter, dead fish, rotting food, etc. It is very deadly, and should not be present in a cycled tank.
-Ammonium is a less deadly form of this compound, ammonia becoming ammonium at low pHs. Ammonium is readily taken up by plants (along with nitrates).
Nitrite is the second form off ammonia found in an aquarium. Not sure what bacteria does this, but ammonia becaomes nitrite through nitrogen fixation, and is less deadly than ammonia.
Nitrate is the third form of ammonia. It is the least deadly, and is usually found in tapwater (meaning that you can have nitrates in your water before it has even begun to cycle).
Phosphates are taken up by plants, so you will need some amount of it in your tank. However, algae also requires it, so if you have a lot of it in your tank, in conjunction with other chemicals and lots of light, you might have algae problems in your tank.
That was all off the top of my head, and chances are there might be some errors. I should be right for the most part. *scratches head*
