Could you explain in simple terms what are the functions of the WH chief of staff and provide the job's analogs in other countries? Is it like the head of the presidential administration (in the European sense of the word 'administration', not in the American meaning of "the government")?
The official title of the role is Assistant to the President and Chief of Staff, which perhaps helps give some insight into the role. It is a political appointment, initially created by an executive order made by Eisenhower in 1953, appointees to which are selected solely by the President, and has no specific codified duties as such. As a consequence of this, these duties tend to change depending on the serving President's demands, but the role generally encompasses a range of advisory and managerial aspects.
For example, the duties of the previous acting Chief of Staff, Mick Mulvaney, included managing the President's schedule and overseeing access to him in the Oval Office, working towards the agenda of the President by negotiating with both Congress and the rest of the executive, and providing advice to the President on policy matters. The Chief of Staff is also responsible for and in charge of all staff working in the White House.
As far as analogous roles in other countries go, the position's amorphous duties makes this hard to answer, but the role is roughly equivalent to positions in the UK such as the Chief Advisor to the Prime Minister, the Chief Whip, the Principal Private Secretary to the Prime Minister, and the Cabinet Secretary. All of these positions have duties which are currently carried out by the Chief of Staff.