Horses are flight animals that startle somewhat easily. When a horse startles while being worked, we say the horse has spooked (US) or shied (UK).
A spooky horse is one that is prone to startling or spooking more easily than others - it's obviously considered a negative trait. A spooky horse will startle at the silliest of things such as, for example, its own shadow, your trainer's bright pink shirt, the click of a camera, etc.
Spooky horses are generally put through some kind of desensitization training to make them less spooky - people can fall off when a horse spooks badly enough, especially if they're less experienced.
Another related term is "looky" - when the horse doesn't startle or spook, but easily gets distracted by things that are going on and starts looking at them not, say, where it's going.
Some spooky horses may actually have anxiety disorders and in extreme situations might even benefit from medication.