Chaps & Gaiters
There are plenty of practical reasons for wearing half-chaps or gaiters over your jodhpurs but, all the sensible stuff aside - they just look so stylish!
On the practical front, though, their main function is protective, not only stopping all that horse sweat from soaking into your jodhpurs but also warding off all the scrapes, scratches and snags you might otherwise be subject to while out hacking along the hedgerows or bridle paths. Many riders also find they protect the calves from pinching or chafing against the stirrup leathers while riding.
Half-chaps also provide added support to the lower leg while in the saddle, much like wearing long riding boots would do, but giving more flexibility to the ankle than would be the case in long boots.