If your ancestor was born on 7 October 1582 then she wasn't in the part of the world (specifically Catholic Europe) for which that day did not exist.
The calendar commonly - though not exclusively - around the world today is called the Gregorian calendar, named after Pope Gregory XIII, although it wasn't he who created it but he had the authority to publish it have it put into use. The previous calendar was issued by Julius Caesar but it had inaccuracies and by the 16th Century it was out of phase with the turn of the seasons - the equinoxes and solstices. To make up the difference ten days were dropped from October 1582 and the day after 4 October 1582 was declared to be 15 October.
It took many years for the rest of Europe to adopt the calendar and if you read histories of this period as I do the dates become a problem. An event in France was ten days different compared with England. Authors have to decide which of the two to observe and some use both. Britain didn't adopt the new calendar for nearly two hundred years - in 1752.
All of this made crossing some borders confusing. We're used to time zones when travelling in the modern world. Mine is ten hours ahead of GMT - or UTC - but ten days ahead is another thing entirely!