An undersecretary is an executive government official in many countries, frequently a career public servant, who typically acts as a senior administrator or second-in-command to a politically appointed Cabinet Minister or other government official. The title is used in many different political systems.
Historical use 
Before 1972, "Undersecretary" (also spelled "Under Secretary") signified the senior deputy to a cabinet Secretary, especially of State and Treasury. The Under Secretary would typically be a political appointee. The office of Under Secretary of State was replaced by the Deputy Secretary of State and the office of Under Secretary of the Treasury was replaced by the Deputy Secretary of the Treasury.
Holy See 
Hong Kong 
In Hong Kong, undersecretary is a position created in 2008 to work closely with bureau secretaries and top civil servants to implement the Chief Executive's policy blueprint and agenda in an executive-led government. The appointment of undersecretaries and political assistants is an extension of the Principal Officials Accountability System into today's Political Appointments System.
In Italy, Undersecretary is a second-in-command to a politically appointed Minister. In particular, he/she is appointed with a President of the Republic Decree, on proposal of the Prime Minister, who previously agreed such proposal with the relevant Minister.
In the Spanish Government, the Undersecretary is a political appointee charged with the daily representation of a ministry, the management of the common services and personnel. The position is equivalent to the British Permanent Secretary. The Undersecretary reports to the Minister, and is appointed by the King on the advice of the Council of Ministers.
United Kingdom 
The title of Under-Secretary is used in two different contexts in the British political system. A Parliamentary Under-Secretary of State is a junior member of the government, always an MP from the governing party, who is appointed to assist a Secretary of State or other government minister. They rank between a Minister of State and a Parliamentary Private Secretary; the rank is usually seen as a stepping-stone to higher political office. In contrast, a Permanent Under-Secretary is a civil servant employed to head part of a government department and oversee the implementation of policy.
United States 
In the United States executive branch, an undersecretary is a senior official in a government department, junior to a departmental Secretary such as the Secretary of State and usually junior to a Deputy Secretary as well. An Undersecretary is typically a career government official, as opposed to a political appointee; they may head specific sub-departments or agencies such as the Defense Intelligence Agency, or be responsible for a specific area of policy within the department, e.g. the Undersecretary for Management within the Department of State.
While the Cabinet Secretary provides vision and direction, undersecretaries run the department and are often considered the government equivalent of a chief operating officer, albeit for a specific branch.
- Mary Ma, "It pays to be forward looking", The Standard, June 04, 2008