Have you ever grown a pepper plant that quickly became a favorite within your garden? Perhaps you planted some pepper seeds and noticed that one of your plants produced far more peppers than your others, or maybe they were bigger or more flavorful. Let's say winter is fast approaching and soon your garden will go dormant. Being a favorite plant, you'll likely want to continue growing it year after year.
You could take seeds from this favorite plant in an attempt to grow it again next year, but there’s no guarantee the next generation of plants will have the same desired traits. Pepper plants can cross-pollinate with one another producing an accidental hybrid. Or, being a "different" first generation plant, even if it were to self-pollinate, each offspring is likely to randomly vary from this parent and potentially have less favorable traits.
While it can be exciting to see new, unexpected pepper plants, it can also be disappointing when the next generation of plants aren't as robust. To compensate, you'd need to grow many new plants and hope at least one plant has the desired traits, so the process can be repeated. Through selective breeding, after about seven generations (if cross-pollination doesn't occur), a stable seed strain could be achieved.
Alternatively, you could dig out this plant to overwinter indoors, bringing it back out in the spring and replanting as a second year plant. Though, it could die or catch the mosaic virus. Each year, we lose 10-30% of our overwintered plants to death or disease. Even if successful, you'll only have one of your favorite plants.
The only 100% certain way to produce new plants that are genetically identical to another is through cloning.
Nearly any plant can be cloned by simply taking a piece of the plant and attempting to get it to root, but the process can be a bit more complicated than just that, as some plants are much more difficult to clone than others.
Keep in mind that not all cuttings will root successfully, so take more than you're planning on using. Everyone has their own method for cloning plants, and some plants are different than others, so try a few different methods before giving up.