Stable means that if conditions vary they will vary in some sort of a cycle, around a range that is acceptable to the livestock and plants.
pH variations based on CO2 is a very good example. Fish do not seem to be bothered by a reasonable variation in the pH, especially the 24 hour cycle, when it is caused by varying levels of CO2.
Mineral levels are a bit more important that changes happen slowly, or not change. Fish osmoregulate based on the minerals and salts in the water. Their metabolism gets set to a certain TDS in the water and it does not change easily. So, if you need to change the TDS, go slow. Optimum is to hold it stable, meaning the same value. What usually happens is the TDS gradually rises. Do a water change before it gets so high that a water change results in too great a drop in TDS.
Temperature is another good example. In nature fish can rise or fall in their habitat to choose the optimum temperature. In an aquarium the whole tank is usually one temperature. If this varies through the day by a couple of *F or about 1*C pretty much all fish are fine with that, and most will handle even larger changes pretty well. Many fish in the wild also experience an annual temperature cycle, too. Especially temperate water fish.
So... stable conditions that are safe for even delicate fish, as long as both ends of the range are within the accepted range for that species:
Stable temperature: +/- 2*F
Stable pH (CO2 related): +/- 1.0
Stable TDS: Rise (harder water) up to 15% change with one water change or lower (softer water) no more than 10% less with any one water change. Changes of this magnitude could be done about twice weekly if the goal is to ultimately change the water the fish are living in.
More durable fish can tolerate more of a range, and over a shorter period of time.
For example, when you drip acclimate fish you are changing pretty much all the parameters over an hour or so.
I prefer to put fish in a quarantine tank that matches the water where I bought the fish, then change the parameters over the month that the fish in in quarantine.