The Privy Council is one of the oldest parts of British Government being over 800 years old. Originally the Monarch
's official quorum
for the great and the good of the land to advise
on how to run the country it is now an odd remant of it's imperial
past in a modern constitutional monarchy
There are three main areas the Privy Council Office still has power over in the modern world.
The Judicial Committee of the Privy Council - once the highest court of law for the British Empire's overseas colonies (25% of the world's peoples) now has adapted to remain the court of final appeal for those Commonwealth countries which have retained the appeal to Her Majesty in Council or, in the case of Republics, to the Judicial Committee. It is also the final appeal court for the Channel Islands, Isle of Man and United Kingdom overseas territories. It also has certain domestic jurisdiction within the United Kingdom, including the function of being the court of final appeal for determining "devolution issues" under the United Kingdom devolution statutes of 1998.
Geographically the Judicial Committee is in separate building, remaining in Downing street, whilst the rest of the JC moved to Carlton Gardens (just off The Mall)
The Secretariat - under the Clerk of the Council the secretariat handles the day-to-day running of PCO. Maintaining the integrity of minor obtuse government issues such as the use of the word "University" in business titles, the application and alterations made to Royal Charters, and the appointment of members to statutory regulatory bodies such as the General Medical Council.
The Ministerial business of the PCO is arranged by the President of the Council who ensures Privy Council business is presented smoothly, and for presenting the draft Orders to Her Majesty for approval at the regular meetings of the Council. It is also a Cabinet Office position usually in modern times combined with the position as Leader of the House of Commons.
N.B. I worked as Webmaster for the Privy Council Office website for 12 months, strange place, like stepping back into the 19th century.