Re: precise measurement of the length of the Saturnian day continues to elude us
what exactly ought to be considered as 'a day'?
A very good question that has baffled planetologists and astronomers for some time. There are currently three dominant, numbered schemes for calculating Saturn's day.
Furthermore, why is it significant?
Day length - or, rather, rotational speed - impacts a lot of Saturn's characteristics. Almost any model of Saturn's atmospheric circulation is dependent on rotation (by way of Coriolis force), as are models of its interior (since rotation has rendered Saturn distinctly non-spherical). Because Saturn's magnetic field rotates with the planet, rotation also impacts its moons through various mechanisms, like the way Enceladus's plumes interact with the planetary magnetic field.
If you're interested in such details about Saturn, day length is significant.