Iacedrom and Ygbir are photorealistic-looking counterparts to Mordecai and Rigby. Their names are "Mordecai" and "Rigby" spelled backwards (with a minor exception; "Rigby" backwards would be "Ybgir"). They both wear top hats and speak very formally.
They met Pops when he came to their domain, Dizzy World, and gave him some ice cream, telling him that they outlaw speeches (which is the reason Pops came there), and that it was also illegal to not enjoy ice cream.
Iacedrom and Ygbir tell Pops to leave because he broke the law by giving a speech. They then decide to kill Pops, but Mordecai and Rigby intervene, helping him escape.