In less colorful language, they mean training is hard work and hard work means working up a sweat. You can assume that wet saddle blankets also mean wet girths, fenders, flaps, reins, headstalls, cheekpieces, and other wet leather parts depending on your sport. Left to dry, that sweat can damage your leather. Dirty leather becomes not only becomes stiff and dry, but the collective grunge can also irritate your horse's skin. Combined with dirt and accumulated grease from gummy leather care products, sweat becomes a breeding ground for bacteria that eat away at stitching weakening it permanently.
Successful training requires a plan.
So does tack care. Make it easy to clean your tack as soon as possible after riding and you're more likely to tend that tack faithfully. Follow a quick cleaning routine after every ride and schedule a more thorough cleaning at regular intervals. Here's how it works. Ideally, your barn has a tack room with a sink close to the cross ties.