An amonia spike is when you test large amounts of amonia in the tank. Usually found during a cycle or when a fish or other livestock dies before the bacteria is capable of handling it and you cannot manually remove it.
NO2 is nitrite and NO3 is nitrate. Ammonia will break down into nitrite and both are toxic to fish. Nitrite will then break down into nitrate. Fish can deal with certain amounts of nitrate, but corals can't.