According to Rebecca Probert in Marriage Law for Genealogists the definitive guide
Key fact: before 25th March, 1754, neither the Church nor the secular courts regarded as valid any marriage that had not been celebrated before an ordained Anglican clergyman.
If your ancestors were not Anglican (e.g. Catholic or non-conformist) they may have wished to avoid attending an Anglican church three Sundays in a row to hear the banns read, which a licence would enable them to do.
A licence would also speed up the marriage process, avoiding a three week delay -- which might be useful if the the couple had 'anticipated the marriage' and didn't want it obvious when they presented themselves to the incumbent.
Prompted by AdrianB38: Furthermore, marriages were not supposed to take place at certain times of the year. For instance, not during Lent. If the couple needed or wanted to marry during one of those periods, they would need a license to do so. And, if I'm reading Probert correctly, marriages were allowed from 13 January, and then at various intervals until the start of Advent (4th Sunday before Christmas). So 6th January was indeed a prohibited date, which is probably your solution. (Why they chose to marry then rather than a week later is worthy of investigation.)