The two years mark what is called Old Style and New Style dates. Prior to 1752, the new year in England and the American colonies started on March 25th. So if the person died on March 24th, 1720, it's ambiguous whether that meant the year that had not ended yet, or the one that started on January 1st (and to add confusion, Scotland started their year on January 1st since 1600). So this person died in the year 1720 or 1721, depending on when you start the year.
The other major change in 1752 was that Britain and her colonies switched to the Gregorian calendar. So Wednesday, September 2nd, 1752 was followed by Thursday, September 14th.