The reason for double-dating

According to the Julian Calendar (which was used by the Pilgrims), the New Year started on March 25, not January 1.  It also declared that a year was 365 days, 6 hours long.  However, in 730 AD, the Venerable Bede, a monk, discovered that this calendar was off by 11 minutes and 14 seconds. Nothing was done about it, however, and over the next 850 years the calendar kept getting further and further off until it was nearly ten days off in the year 1582. Pope Gregory XII declared in 1582 a new calendar would be used, named the Gregorian calendar, which would fix the problem.

However, much like the metric system and the United States today, people were resistant to logical change. The new calendar was adopted immediately by France, Italy, Spain, Portugal and Luxembourg, and within a few years by Germany, Belgium, Switzerland, and the Netherlands. But it wasn't until nearly 200 years later that the calendar was adopted by the British government (and thus the American colonies).

The British Parliament decreed that September 3, 1752 should be renamed September 14, 1752, which would fix the eleven day discrepancy; and further, they ruled that January 1 would be the beginning of the new year--it would no longer be March 25. The Russian Orthodox Church, and several mid-east countries are still using the Julian calendar even today. The Julian calendar is nearly half a month off now.

To make matters worse, while dates in the 1700s are 11 days off, dates in the 1600s are just 10 days off.  So, when the researcher goes looking at records written in the 1600's, they will find the dates are by the Julian calendar, not our present-day Gregorian calendar.  To note this, many times the date is written 1 March 1692 (O.S.) which stands for "old style", or 11 March 1693 (N.S.) which stands for "new style".  Other sources, such as this web page, will simply write that same date as 1 March 1692/3, to indicate it was 1692 to them, but 1693 by our present-day calendar.  Of course, this does not take into account the ten days the calendar was off, so the date is also sometimes written like 2 March 1692 / 12 March 1693.  

For a more detailed explanation on the calendar differences, I refer the reader to an article titled "Old Style vs. New Style" in The Mayflower Descendant, 1:17-23.