Rabadon's Deathcap is essential for any champion with ability power ratios, tanky or carry, wishing to deal significant magic damage that will carry into late game.
Depending from the champion's base damage and/or ability power ratios, however, Void Staff may be a better purchase.
Champions with high base damage will generally benefit more from Void Staff, especially if they have low ability power ratios. But a champion with high ratios but low base damage, such as Kassadin or Fizz, will benefit more from Rabadon's Deathcap.
Rabadon's Deathcap's passive stacks multiplicatively with Archmage. The two combined increases ability power by 36.5%.
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 on 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, to the point of the item being barely cost effective, which the large majority of expensive items are by a large margin.
It is also somewhat difficult to build early in the game as one of its components is quite expensive, making it difficult to purchase without kills or other gold income.