The phrase "mount up" means to climb up onto the back of. Synonyms include climb on, get on, mount, hop on, jump on, bestride etc. It was used in reference to mounting a horse. The word "mount" was used as a reference to the animal itself, not necessarily a horse, but some animal the person rode and "up" meant on top of it. The most applicable use was however when referring to getting seated in ones saddle on ones horse. It was a common order issued in horse cavalry companies in the military. When a period of rest was over, some action forth coming or an order to mobilize came through the first order issued was to mount up, or in other words to be ready to move.
