The History of Animation

 Eadweard Muybridge
Eadweard Muybridge studied the movement of many things, especially animals.  His work was seen as a major step forward to modern-day animation. Perhaps his most well know projects was the "Horse in Motion":

In 1872, former Governor of California Leland Stanford, a businessman and race-horse owner, had taken a position on a popularly-debated question of the day: whether all four of a horse's hooves are off the ground at the same time during a gallop. Up until this time, most paintings of galloping horses showed the front legs extended forwards and the rear legs extended backwards. Stanford sided with this assertion, called "unsupported transit", and took it upon himself to prove it scientifically. Stanford sought out Muybridge and hired him to settle the question.

Muybridge used a series of large cameras that used glass plates placed in a line, each one being triggered by a thread as the horse passed. Later a clockwork device was used. The images were copied in the form of silhouettes onto a disc and viewed in a machine called a Zoöpractiscope. This, in fact became an intermediate stage towards motion pictures or cinematography.

 In 1877, Muybridge settled Stanford's question with a single photographic negative showing Stanford's racehorse Occident airborne in the midst of a gallop. This negative was lost, but it survives through woodcuts made at the time. By 1878, spurred on by Stanford to expand the experiment, Muybridge had successfully photographed a horse in fast motion.

This series of photos taken in Palo Alto, California, is called Sallie Gardner at a Gallop or The Horse in Motion, and shows that the hooves do all leave the ground — although not with the legs fully extended forward and back, as contemporary illustrators tended to imagine, but rather at the moment when all the hooves are tucked under the horse as it switches from "pushing" with the back legs to "pulling" with the front legs. This series of photos stands as one of the earliest forms of videography.

-Wikipeadia

At the bottom left of this video, the numbers of each picture (frame) can be seen

Zoetrope
Animation dates back to as early as 180 AD when the first Zoetrope was created in China. The modern version of the zoetrope (which is more well known) was created in 1834 by George William Horner. A Zoetrope is a cylinder with lots of pictures on the inside that spins.  There are usually slits in the side of the cylinder so when you look through, it gives the illusion of movement.

Here is a modern-day example of a large, 3D zoetrope with flashing lights to create the illusion of movement: