Breeding is a disparate art, since it is a partly passive, partly fortuitous talent requiring highly developed Farming skills. The first stage of breeding is to possess two healthy adult animals - livestock for instance - and to have them procreate. This can be induced if you have the skill. After intercourse the mother must be well-tended (feeding and protection) over the pregnancy period and eventually she will give birth. It is important, during the birthing process, that she is attended, healed and cared-for to ensure successful delivery. The end-result will be offspring, new life, an increase in the herd or flock. Detailed information on birthing, animal raising and such can be found in your AB FARMING lists - if you have the skill - or, in summary, under HELP FEEDING.
There are many advantages to breeding, to growing one's herds and flocks. Some will use their skills for purely financial ends: leather hides for commodity processing, meat for future slaughter, wool from fleece, etc. Others will breed for military reasons, to train up steeds for a city or guild's cavalry. Some even breed animals for pleasure; for the joy of spreading life, to fill the world with more vigour, colour and natural abundance. This choice rests entirely with you.