It's basically a tamagotchi.
You buy a starter pack, get X number of random breedables (we'll call them pets) though guaranteed to have at least 1 male and 1 female. Food, etc. The pets eat food, drink water, or whatever other rules you program them with. If a male and female are happy, well fed, or whatever coded parameters you put in, they fuck and make a baby. The baby will inherit traits through their gene line (up to 4 generations back usually) through a complex math formula, and then said baby can be sold on second hand marketplaces or whatnot or kept for yourself.
The business model here is that the pets all need food/water/etc to survive, so the player needs to keep buying expendable items. Additionally, there might be other "boosters" you can sell, if you code your system for it, of course.
A good breedable will have system where there's a huge amount of possibilities, and many unique/rare/special one-time features, and one where the player can control it to some extent.
This seems silly, but if you play path of exile, it's like fossil crafting, but imagine a resonator with 12 sockets, but instead of creating an item with 6 traits, you're creating a breedable pet with 6.
Some of the common breedables on SL are --
Fennux Breedable - Official Website - home
www.fennux.com
Amaretto Breedables Network - Landing Page (These were the people involved in that
famous court case about virtual items)
www.worldofmeeroos.com
All these fucking people make 10 times what I do prolly, though they are teams of multiple people. One person can't run a successful breedable company.