What is the royal prerogative?

The royal prerogative is the residue of power, inmunity and privileges which remains with the Crown (in other words, the power the Crown has which it can use without an Act of Parliament requiring it to do so). Over time, as British society has evolved and parliamentary democracy has expanded, the Crown's power has decreased, but it still encompasses things such as 

(a) International treaties (although the enactment of those treaties has to be ratified by Parliament)

(b) Declarations of war

(c) The prerogative of mercy (the Crown can stop a convict from being punished, although the conviction itself remains)

(d) The granting of honours.

Traditionally, the powers within the prerogative are not subject to judicial review.