Along with it's sound, Sgt. Pepper also made a visual impact. The stunning cover by pop artist Peter Blake depicted the Beatles--decked out in brightly colored band uniforms--standing in a crowd of political, religious and pop culture icons (including their earlier selves in the form of wax dummies from Madame Tussuad's). To see who all was included, check out this annotated chart. There's also more information on each of the figures featured here.
The album cover also featured a gatefold photo of the band and, inside the sleeve, a cardboard sheet with cutouts of military shoulder stripes, a mustache, Sgt. Pepper badges and a portrait of Sgt. Pepper himself. The record came in a pop-artish LP sleeve with pink "blobs" on it created by Dutch designers the Fool and a cardboard sheet of cut-outs.
Perhaps most notably, the lyrics for every song appeared on the back cover--a rarity for the time period.
Here's a video of designers talking about Blake's cover design: