A "cycled" tank is a tank in which there is, generally speaking, enough nitrobacter to metabolize the ammonia and nitrite in the tank.
Remember from grade school how you'd learn about the the balance of the food chain? How the deer would flourish, which would give the wolves lots of food, so the wolf population would grow, but then there so many wolves that the deer population would drop off and a lot of wolves would starve, which would mean fewer deer would be eaten, so the population would grow, and the process would start over again. Over time it settles out to an equilibrium, and the fluctuations all but disappear (barring any outside influence)
The same thing happens in your tank, just replace "deer" with "ammonia" and "wolves" with "bacteria".
There are a couple other fluctuations that stabilize after a few months.
In my opinion, an "established" tank is a cycled tank that's been running long enough to minimize those fluctuations.