Until 1752 in England the 1st January was not the start of the new year but Lady day on 25th March. So each year ran from 25th March to 24th March.
Usually the two years are given in modern indexes and sometimes in the actual parish register itself. In the C17th their calendar was the Julian calendar so they knew which date they were on, but were also aware of the Gregorian calendar date
When the change was finally made to the Gregorian calendar in 1752 (Scotland changed much earlier) which is more accurate, the calendar was so far out that 11 days had to disappear.
The start of the year at Lady day is still with us - its called the start of the financial year = Lady Day + the missing 11 days.
http://www.adsb.co.uk/date_and_time/calendar_reform_1752/Regards
Valda