In political conversations with Americans, they often want to impeach the leader of the other side. Unlike countries like Canada or Israel, however, where courts can charge a leader with a crime, the American system offers its president and head of state, immunity from such legal recourse. The leader can eventually be charged with crimes after his/her term has ended; but, not during.
In most parliaments the Prime Minister is not that different from other elected ministers. Like them, he represents a single riding (or district, as they call them in the US). In a country like Canada, it's the party, its policies, loosely tied together by an ideology, and the Prime Minster combined, that's elected by the population. The PM, btw, can be defeated in his/her local riding/district race.
In USA the districts and the president are given power in separate elections. The White House and the House of Representatives (along with the senate) stand in political opposition to each other as checks against each other.
Removing a president from office is based on two 2/3 votes: one from the House of Reps ...the impeachment... and one from the Senate...the conviction. That is, the check on his leadership is vote based, that is, it's a political mechanism, not a rule of law based one. And this is why, I like to argue, the American system is not based on rule of law; but rather, a system based on balance of power.