Definition

a device that produces the illusion of motion from a rapid succession of static pictures inside a spinning cylinder with vertical slits.

Extended Definition

The zoetrope consists of a cylinder with slits cut vertically in the sides. On the inner surface of the cylinder is a band with images from a set of sequenced pictures. As the cylinder spins, the user looks through the slits at the pictures across. The scanning of the slits keeps the pictures from simply blurring together, and the user sees a rapid succession of images, producing the illusion of motion. (source: Wikipedia)

Links

• Howcast Video - How to Create a Zoetrope

Study Guide & References

Above is a Cartoon Network bumper which gives a good example of a Zoetrope in action
Above, Disney took the concept of a Zoetrope to 3d to illustrate how animation works.

History:

The zoetrope was invented in 1834 by William Horner, who originally called it a Daedalum ("wheel of the Devil"). It was based on Plateau's phenakistoscope, but was more convenient since it did not require a viewing mirror and allowed more than one person to use it at the same time. Horner's invention strangely became forgotten for nearly thirty years until 1867, when it became patented in England by M. Bradley, and in America by William F. Lincoln. Lincoln renamed the Daedalum, giving it the name of "zoetrope," or "wheel of life." 

How it works:
The zoetrope is the third major optical toy, after the thaumatrope and phenakistoscope, that uses the persistence of vision principle to create an illusion of motion. It consists of a simple drum with an open top, supported on a central axis. A sequence of hand-drawn pictures on strips of paper are placed around the inner bottom of the drum. Slots are cut at equal distances around the outer surface of the drum, just above where the picture strips were to be positioned. 

To create an illusion of motion, the drum is spun; the faster the rate of spin, the smoother the progression of images. A viewer can look through the wall of the zoetrope from any point around it, and see a rapid progression of images. Because of its design, more than one person could use the zoetrope at the same time. 
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What became of it:

This zoetrope offered two improvements on the previous phenakistoscope. First, the zoetrope did not require a viewing mirror. The second and most influential improvement was that more than one person could view the moving pictures at the same time.

However, when the praxinoscope was invented 1877, interest in the zoetrope declined. Finally, in 1895, modern cinema was born. Once moving pictures could be projected on a large screen, optical toys such as the zoetrope became used less and less frequently.

Source:
http://courses.ncssm.edu/gallery/collections/toys/html/exhibit10.htm