Prior of the creation of Toy Story, the standard for animated films were Two-Dimensional (2D) usually hand drawn films. Companies like Walt Disney Animation released various 2D films that are still beloved today including Snow White and the Seven Dwarfs and Cinderella. During the time, Three-Dimensional (3D) stop motion films were being produced too. However, Pixar took the next leap of advancement when they created 3D animation software that could be fully processed and rendered in a computer.
Frame of "The Adventures of André & Wally B" by Pixar (1984)
Pixar was a new company that worked in making short 3D films for advertisments,their first 3D short film being The Adventures of André & Wally B. It was the first example of fluid character animation in the beginning years of computer animation.
Luxo Jr. by Pixar (1986)
Pixar built new software for 3D animating and rendering including Renderman and Presto. Both softwares allowed the animators to easily control characters and other things. With the use of 3D software, they could add details onto chraracters and background with much more ease.
Pete Docter working on Toy Story