Rabadon's Deathcap is essential for any champion with ablility power ratios, tanky or carry, wishing to deal significant magic damage that will carry into late game.
This item resulted from a separation of the offensive and defensive abilities of Zhonya's Ring. This is the offensive item, while Zhonya's Hourglass is its defensive counterpart.
It was originally named Banksy's Deathcap in the Patch Day Preview. This is a tribute to one of Riot's employees named Banksy (David Banks, Director of Platform Engineering).
The image artwork would seem to be based off of the Sorting Hat from the Harry Potter franchise. There are eyes and a mouth-like band visible on the hat, very similar to the Sorting Hat.
While it has the potential to be the single highest source of ability power in the game, Rabadon's Deathcap is rarely purchased first, as its passive ability requires other ability power items to be fully effective.