I come from a land of sheep (New Zealand) and now I live in another (Wales). Sheep are not only important in the cultures and economies of both countries, they also figure in many aspects of our daily lives. We wear clothes made from their wool, use products made from their leather and, in the English language, we regularly use many sheep-based idioms.
If you’re feeling sheepish, you’re embarrassed because you know you’ve done something silly or wrong. You might be the black sheep of the family, the one who’s different, perhaps disreputable, maybe unloved. You should beware the wolf in sheep’s clothing, the dangerous person who’s pretending to be harmless. If you work as a manager, you might need to separate the sheep from the goats, i.e. separate those people who are competent and worth keeping from those who are not. If you fancy someone but feeling shy and a little foolish, you might make sheep’s eyes at them. And if you’re having trouble getting to sleep at night, then you could always try counting sheep!