In the most basic terms, the ammonia and nitrites have spiked and eventually read as undetectable. It indicates the presence of nitrifying bacteria (nitrosomonas & nitrobacters respectively) which convert these to a much less harmful nitrate. The tank will continue to go through many changes (ups & downs) for many months afterwards.
Once the initial formation of bacteria form and stabalize, the tank should be able to support sturdier forms of life. Once denitrifying bacteria form (facultative anaerobes) the tank will be able to support more sensitive and complicated forms of life. That end of the process is much slower and can generally take many months to a year depending on the tank set up.