Nitrogen Cycle - New Tank Cycling

Like all living creatures, fish give off waste products. These nitrogenous waste products break down into ammonia (NH3), which is highly toxic to most fish. In nature, the volume of water per fish is extremely high, and waste products become diluted to low concentrations. In aquariums, however, it can take as little as a few hours for ammonia concentrations to reach toxic levels.
How much ammonia is too much? The quick answer is: if a test kit is able to measure it, you´ve got too much. Consider emergency action (water changes and zeolite clay) to reduce the danger.
The nitrogen cycle, more precisely, the nitrification cycle, is the biological process that converts ammonia into other, harmless nitrogen compounds. Fortunately, several species of bacteria do this conversion for us. Some species convert ammonia (NH3) to nitrite (N02-), while others convert nitrite to nitrate (NO3-).
So, cycling the tank refers to the process of establishing bacterial colonies in the filter bed that convert ammonia -> nitrite -> nitrate.