The name Williams is most usually of Welsh origin having been brought to the country by settlers, especially during the seventeenth century. The name became widespread to such an extent that descendants bearing this name can be found in every county in Ireland.

William is a popular proper name of old Germanic origin. It became very popular in the English language after the Norman Conquest of 1066, and remained so throughout the Middle Ages and into the modern era. The modern German equivalent is "Wilhelm." It is sometimes abbreviated "Wm."

William is derived from the Norman language, and of Germanic origin: "wil" = will, desire; "helm" = helmet, protection. The Old German name Wilhelm and the Old Norse name Vilhjálmr have the same roots. The Belgian name "Guildhelm" means "harnessed with a gilded helmet".

The oldest known famous bearer of the name was Saint William of Gellone; his cult spread the name throughout Europe.

According to the 1990 U.S. Census the name William is the 5th most popular first name with 2.451% of the male population (around three million). The last name Williams is the 3rd most popular last name with 0.699% of the population (around 1,747,500 people).
From Wikipedia