Lets be clear here.
F1 is a genetic term referring to first generation offspring between two parents. For example, lets say you cross plant A with plant B. All the hundreds (or thousands) of resulting seeds you get from this cross would represent "F1" plants.
Cross two F1s, and you have an F2. Cross two F2s, and you have an F3, etc.
Now, whether or not a particular strain is "stable" is **NOT** the same thing as F1, F2, etc. A more precise term used for this in conventional breeding is "true-breeding"
That means if you cross two parents of the same strain, the offspring will all be exactly the same as the parents. In this case, the strain is "true". Genetically speaking, it means that all of the plants genes (or all of the important ones) are homozygous at each locus, or nearly so.
So for the truly established strains, like Northern Lights, Skunk #1, etc, not only should all the seeds in a pack give you similar plants, but crossing them with one another should yield offspring that are also similar. Cross two F1s, and the F2s should be similar. Cross an F2 back with a parent, and again, you end up with something similar. No matter how you do the crosses (F1xF3, F2xparent, F4xF8, etc), if you're working with actual true-breeding stains, you should end up with offspring similar to the original plants. That's what people mean by "stable".
The problem arises when you cross DIFFERENT plants. Lets say you crossed Northern Lights x Skunk #1. The offspring (F1) of this cross are all likely to be similar, or at least considerably similar since they'll each have roughly identical half-genetics from each parent. IE they're HYBRIDS. But when you cross the F1s to get an F2 and now these F2 plants are likely to be considerably different one from the other: some taller, some shorter, some bushier, etc. They'll have random combinations of traits from each of the original parents. They're not "true breeding" because the genetics have not been stabilized.
And this is one of the "dirty" little secrets of commercial cannabis breeding.. .many of the so-called "strains" for sale aren't really "strains" at all, but F1, F2, or later hybrids created from other true-breeding (and in some cases NOT true-breeding) strains. And that's why they're not stable. If they're F2 hybrid plants, you would expect that multiple seeds in a pack would grow up to be plants with different traits.
How do you stabilize? Basically you cross a plant again and again with the same parent until the genes all become the same (homozygous) at each locus, and the variation goes away.
There are several problems with this approach though. The first and most important is that it takes many generations of crosses (at least 5 and 10 is better) before you end up with something reliably stable. That's potentially going to take 1-2 *YEARS* of crossing with careful selection if you're working indoors, and many years if you're working outdoors. So you can see why breeders might not like to do this. . .its hard work!
The next major problem is that some traits require mixed genetic combinations to be expressed. In other words, certain traits REQUIRE hybrid genes, and in cases like that, the plants simply CANNOT be stabilized. Cross plants like this, and not only will you get many different traits in the offspring, you may end up with NONE of them that are close to what you started with!
The real-world solution to this issue is that when you find that "super-plant" that you love, if its a hybrid, then the only reliable way to get more plants exactly like it would be to clone it. That's why some of the elite strains are "clone only". . .they're hybrids that cannot be stabilized via crosses (or in some cases, unique hybrids where a similar male plant cannot be found). .
Hope that helped a little.
