Breeding creatures (those with the necessary CHILD tokens) can produce offspring in fortress mode. Conversely, non-breeding creatures cannot reproduce in fortress mode, even though they may do so during worldgen (e.g. dragons). Breeding creatures are significantly more useful as stock for a meat industry than their non-breeding counterparts.
When a male and a female of the same breeding species are present on the map, sooner or later the male will impregnate the female. Animal reproduction requires absolutely no contact between them, and in fact will occur regardless of distance, physical obstacles such as walls or locked doors, number of each gender, and even ownership. This has been jokingly referred to by players as spore-based breeding; even a male in a herd of wild animals outside the fortress walls can impregnate a female locked deep in the lowest level, and females can get pregnant again immediately after giving birth (much like dwarves). The only thing that has been reported to prevent pregnancy is caging, but females that are already pregnant can give birth while caged (also much like dwarves).
There is currently a per-creature-type population cap, observed to be around 50, past which breeding animals will not get pregnant; existing pregnancies will mature to term. Once the population drops below the cap, the creatures will begin breeding again.