What is the significance of the number 111111 as it is applied to holiday?

The Armistice ending World War I was signed on November 11 at about 11 am: the 11th hour of the 11th day of the 11th month.

For years this was celebrated as Armistice Day. After World War II the name was changed in the US to "Veterans' Day" and in much of the British Commonwealth to "Remembrance Day".