What does it mean to cycle an aquarium?

Cycling an aquarium means growing the beneficial bacteria that handle fish waste. Fish poop and leftover food break down into ammonia, which is toxic even at low levels. During a cycle, bacteria build up that convert ammonia into nitrite (also toxic), and then into nitrate, which is much safer and can be controlled with water changes and live plants. In practice, a tank is "cycled" when it can process a full day's worth of waste without dangerous spikes. With a liquid test kit you'll see ammonia and nitrite rise and then drop to 0 ppm, while nitrate shows up (often 5-40 ppm). For most new setups this takes about 3-6 weeks, faster if you seed the tank with established filter media, and sometimes longer if the tank is cold or you don't have much surface area in the filter. Most people cycle either fishless (add an ammonia source and test every few days-safest for fish) or with fish (small stocking, feed lightly, and do frequent water changes to keep ammonia and nitrite under about 0.25 ppm). Once you're cycled, try not to replace all your filter media at once or deep-clean everything the same day, because that's where a lot of your bacteria live.