Welcome Mike J!
Based on the answers given, you're probably wondering what is meant by stability.
The easy explanation is that if you have time to observe your tank over a given period, you will be able to watch the levels of the various natural occuring elements (nitrates, nitrites, ammnoia, ph etc). The more "stable" these elements are, the more hospitable the environment is for your fish.
Imagine walking into your house one day and none of the lights work. You may get a flashlight, get them to work or merely tolerate it. The next day when you come home from work, your sink is backed up and the whole house smells like sewer gas. The next day you come home, the thermostat doesn't work and you end up freezing all day. These are elements to your home, and admittedly, living with these types of conditions would be unsettling.
It's the same thing with your fish. Since they "breath" in the environment they are living and swimming in, the less stable the elements are in the water, the more stressed they will be.
Some fish like damsels and clows tolerate a remarkable variation in water quality. Some, like angels or hippo tangs have a very low window for tolerance.
Having your tank set up for a longer period of time allows the tank to stabilize all of the elements and make the environment more hospitable for your fish.
Hope this helps you understand things a bit more. Keep asking questions, if you don't, you never get answers!
