The Apostle Paul writes about head-coverings in 1 Corinthians 11. As we try to apply his teaching to our own time it is very important for us to understand the culture that the apostle Paul was writing into.
In Greece during the 1st century the clothes men and women wore were very similar in style apart from the head-covering which was only worn by women. The uncovered hair of a woman was considered sexually arousing and was believed to provoke lust in men. So it was normal, dignified and socially appropriate for women (especially married women) to wear the head-covering.