Short answers, pulled from the story.
Cutout animation is a form of stop-motion animation using flat characters, props, and backgrounds cut from paper, card, stiff fabric, or photographs. The pieces are moved frame by frame under a camera to create the illusion of motion. The technique is closely related to shadow play, with stop motion replacing the live manipulation of flat puppets.
El Apóstol (1917) by Italian-Argentine cartoonist Quirino Cristiani is recognized as the world's first animated feature film, and it used cutout animation. Those prints no longer survive. The world's earliest surviving animated feature, Die Abenteuer des Prinzen Achmed (1926) by Lotte Reiniger, also used cutout animation, with backgrounds composed of blown sand, painted material, and soap.
Before 1934, Japanese animators used cutout techniques rather than cel animation because celluloid was too expensive. Noboru Ofuji was the leading Japanese cutout animator of this era, working primarily in the form and using chiyogami (Japanese colored paper) in films such as Burglars of Baghdad Castle (1926).
Terry Gilliam animated the cutout sequences in Monty Python's Flying Circus, which ran from 1969 to 1975, using ready-made imagery in a collage photomontage style rather than purpose-built figures. He used light from above rather than below, giving his work a flat, opaque quality different from the backlit silhouette tradition. He also directed the 1974 short The Miracle of Flight using cutout techniques.
Michael Jackson's "Leave Me Alone" (1989), animated by Jim Blashfield, won a Grammy Award, a Cannes Golden Lion, and an MTV Award. Blashfield also used cutout animation for Talking Heads' "And She Was" (1985), Paul Simon's "Boy in the Bubble," and Tears for Fears' "Sowing the Seeds of Love" (1989), which won two MTV Awards.
South Park began in 1997 using construction paper cutouts for its pilot episode before switching to PowerAnimator software and later Maya. The visual style was always intended to resemble the original paper technique. South Park: Bigger, Longer and Uncut (1999) and Imaginationland: The Movie (2008) both used computer animation to imitate the cutout look.