Plato explained it thus: The truth is not 'out there' but 'in here'. In the beginning all horses were the same, alike. Although really not one of them was exactly like any of the others. None of them were completely alike neither in a way nor in a sense. All horses had something in common. What all horses have in common is that we call them horses.
Aristotle agreed with Plato in that the actual form of the horse is eternal and immutable. But the 'idea' of a horse was simply a concept that we humans had formed after seeing a certain number of horses. The 'idea' or 'form' horse thus had no existence of its own, no separate independent existence so the 'idea' or the 'form' of horse was made up of the horse's characteristics - which define what we today call the horse species.
Simple really when you think about it.