The Prime Minister of the Daleks was the leader of the Parliament of the Daleks. This particular Dalek did not wear any sort of battle armour but instead situated itself in a clear glass tube. (DW: Asylum of the Daleks)
Biography
The Prime Minister ordered the abduction of the Doctor and his companions Amy Pond and Rory Williams summoning them to the Parliament of the Daleks and granting them a mission to lower the indestructible Force field of the Dalek Asylum.
Once this had been achieved by the human-turned-Dalek, Oswin Oswald, the Parliament launched an attack to destroy the Asylum. The Prime Minister's memory of the Doctor had been wiped by Oswin, along with the rest of the Daleks. When the Doctor came back to their ship, he was bombarded with "the First Question" ("Doctor Who?") by the Prime Minister and the rest of the Parliament. He left shortly after. (DW: Asylum of the Daleks)
Behind the scenes
The Prime Minister of the Daleks marks the first time a Kaled mutant has been seen on-screen since the insane Dalek Caan in the Series 4 finale, The Stolen Earth/Journey's End. Though an Emperor Dalek with an exposed mutant was seen in the Adventure Game, City of the Daleks.