A meta that isn't defined by flavour of the week trends that dominate the ladder (and exasperating the need for balance measures/suspect testing), but rather, something that can be considered consistent and, for the most part, fair for the variety of major playstyles. Moreover, a stable meta means that if you develop a solid team, you can bring it in and expect it not to be made invalid by some new threat or ban come the week/month after.
Most importantly, we know we have a mostly stable meta when Arcanine is no longer considered viable.
Usually, a stable meta will emerge once the power creep of every new release has been dealt with, and the offending forces removed from the tier. But near the release of a new title, things are quite volatile, as one top tier threat is often simply replaced by another once the first is banned, and its difficult to really see how the new meta will change once certain offending threats are gone. Likewise, some things (see: BP) can end up sneaking up from just below the surface, and these things can take time to notice, but when realized, can cause further unforeseen shifts in how the meta works.
Keep in mind that a stable meta does not necessarily imply one without dynamism. The meta will grow, change, and adapt over time, but at a slower, healthier pace that is not built around knee-jerk reactions to wildly powerful threats, but rather around new tactics and strategies, which is generally less prone to stagnation.