Sheep breeding

Ewes are "joined" or mated to a ram (so you know the sire) or to a small team of rams (to ensure that you don't have an infertile ram and so no lambs). All the lambs inherit genes from the ram, so you should pick a ram with the best possible genes - 'The ram is half the herd'. Twins lambs are whole siblings, and all the other progeny of the ram will be half-siblings. Twins lambs are always fraternal, not identical.
Ewes have an ovulation cycle of seventeen days. The ram mates with them several times during the couple of days they are fertile ('on heat'). Lambs are born about 150 days later. Some farmers leave the rams in all the time, but prime lamb breeders usually use a six week joining period so that the lambs are born close to each other and will be a similar weight for sale. Small farmers may also choose a short joining period so they know when to look for lambs.
Sheep, like humans, have DNA in two strands, one inherited from the sire and one from the dam. Each parent passes a selection from both its own strands to its lamb, so the lamb has a new combination pair of genes at each point on the strand. Sometimes one gene in the pair is defective, but normally the good gene is dominant and the defective gene is recessive, so the lamb won't show any genetic defects.