Minister

A person known in politics as a Minister is described by thefreedictionary.com as a:

1. A high officer of state appointed to head an executive or administrative department of government.
2. An authorized diplomatic representative of a government, usually ranking next below an ambassador.
3. A person serving as an agent for another by carrying out specific orders or functions.

They are lead by a Prime Minister and some can form a cabinet run by the Prime Minister and bound by Cabinet collective responsibility. 

Source- http://www.thefreedictionary.com/minister

There are '5 key ministries' of a Western style government.

1. Chancellor of the Exchequer\Treasury Secretary\Fiance Minister\Financial Affairs
2. Secretary of State for the Home Office\Home Department\ the Interior\Home Affairs\Interior affairs
3. Secretary of State for Foreign Office\Foreign Affairs\ Secretary of State
4. Secretary of State for Defense
5. Secretary of State for Justice or Secretary of State for Health (depending on nation, era and circumstances)

Typical cabinet can be any mixture of the below ministers and Secretary of States plus the Prime Minister-

1. Prime Minister
2. First Lord of the Treasury\Chief Treasury
3. Minister for the Civil Service
4. Chancellor of the Exchequer\Treasury Secretary\Finance Minister\Financial Affairs
5. Secretary of State for the Home Office\Home Department\ the Interior\Home Affairs\Interior affairs
6. Secretary of State for Foreign Office\Foreign Affairs\ Secretary of State 
7. Secretary of State for Defense
8. Secretary of State for Justice
9. Paymaster General
10. Postmaster General
11. Attorney General
12. Secretary of State for Education
13. Minister for Women and Equalities
14. Minister for Utilities and Infrastructure (during a major period of infrastructure development, major repairs after a war, major repairs after a disaster like an earthquake or during the mass upgrading of a mostly underdeveloped 3rd World nation like Nigeria).
15. Minister for Information
16. Minister for Science
17. Minister of Propaganda (usually during wars or in collapsing dictatorships)
18. Minister of State Works and Building Projects
19. Minister for oil (in oil rich places like Saudi Arabia and Venezuela).
20. Minister for mining (in mineral and coal rich places like S. Africa and Kazakhstan).
21. Secretary of State for the Regions
22. Secretary of State for the Colonial and Dependent Territories
23. Minister for Homeland Security
24. Minister for Cyber Security
25. Minister for the Frontier Security\Borders\Border Agency\Border Integrity\Border Security (usually during wars, smuggling upswings or in collapsing dictatorships).
26. Secretary of State for Agriculture and Fisheries
27. Secretary of State for International Trade
28. President of the Board of Trade\Domestic Trade
29. Secretary of State for Energy
30. Secretary of State for Industry
31. Secretary of State for Environment
32. Secretary of State for Housing
33. Secretary of State for Aviation
34. Secretary of State for Procurement\Armaments\Munitions\War Effort (during wars).
35. Secretary of State for Production
36. Secretary of State for Telecoms\Telecommunications (during a major period of infrastructure development, major repairs after a war, major repairs after a disaster like an earthquake or during the mass upgrading of a mostly underdeveloped 3rd World nation like Nigeria).
37. Secretary of State for Employment\Labour.
38. Secretary of State for Health
39. Secretary of State for Social securities and Pensions
40. Secretary of State for Transport\Transportation.
41. Secretary of State for Communities and Local Government
42. Secretary of State for Rural Affairs
43. Secretary of State for Food and Water Supplies (often drought and famine hit lands like Ethiopia and Somalia).
44. Parliamentary Under-Secretary of State for Overseas aid
45. Parliamentary Under-Secretary of State for Environmental issues and recycling
46. The 'City' Minister A unique UK post for monitoring the London financial district which the British call "The City".
47. Secretary of State for International Development
48. Secretary of State for Culture, Media, Tourism and Sport
49. Minister for the Cabinet Office
50. Ministry of Electronics & Information Technology In rapidly developing nations like India
51. Ministry of New and Renewable Energy