I’m an American and not familiar with UK’s Parliament. However, I know that the Prime Minister is chosen from the elected MP’s in the House at a given time.
When PM Cameron leaves later, does he have to also step away from his post as MP? Or will he be allowed to remain.
He would be allowed to remain.
He is the elected parliamentary leader of the Conservative Party and de facto Prime Minister as the Conservative Party won a majority of the seats in Parliament and therefore formed the Government. The Conservative Party elected David Cameron as their leader through a process outlined in this answer. He has resigned as the Prime Minister (leader of the Parliamentary Conservative Party).
He is an elected Member of Parliament as voted by his constituency; he has not resigned his seat in Parliament, so he will continue to be Member of Parliament, albeit as a backbencher, with no official governmental office but with full voting rights. He could still be asked to join the Cabinet (front bench) in a ministerial capacity.
Although @BeaglesEnd's answer is effectively correct, it skirts around some of the foibles of the UK's political system.
For example, it is not actually possible to resign as a Member of Parliament. It does happen in practice, Sadiq Khan did recently when he won the Mayoralty of London, but it requires a legal fiction to arrange (he was given the Stewardship of the Chiltern Hundreds). David Cameron did not resign as a Member of Parliament and he has made no indication that he will so.
Also, there is no official job of Prime Minister. What David Cameron has resigned from is leading Her Majesty's Government. He did this by tendering his resignation to the Queen on Friday, 24th June 2016. So he has actually resigned.
He will, however, remain leader of the Conservative Party until a new leader is in place. The process for replacing the leader is not decided by David Cameron but by a group called the 1922 Committee. They have decided the rules (which are the same as when David Cameron was elected) and have stated that the process will be completed by 2nd September.
That new leader will take over as head of Her Majesty's Government. Note, although the Conservative party is the majority in Parliament, that's not actually required to form a government. Effectively, what is required is support from enough MPs, from whatever parties, in order to be able to win a No Confidence vote. It usually helps to have a majority but not always (as members of your own party may vote against you).
The UK system is very different from the US presidential system. Here we do not directly vote for a Prime Minister in the same way that the US votes for a President.
The convention is that the leader of the Parliamentary party with an outright majority is invited to form a government by the monarch although this is not always straightforward. Indeed as in the 2010 election failing to secure a majority does not, in of itself, remove the incumbent Prime Minister.
It is also entirely possible for a majority party to elect or appoint a new leader during a Parliament, this happened with Gordon Brown and there are no constitutional or legal bars to how a party leader is elected and different parties have their own individual systems.
It is even possible, in some circumstances for the Prime Minister to come from a minority party and the last government was composed of a coalition of two different parties. In the UK coalitions are rare but in some European countries they are the norm.
It is also worth noting that, in theory, the Prime Minister is appointed by the Monarch and indeed David Cameron will ultimately formally present his resignation to the Queen not Parliament.
Also unlike the situation in the US there is a substantial overlap between the elected legislature and the executive (the cabinet) composed of ministers, secretaries etc.
The Prime minister must, by convention, be a member of parliament, although historically several modern-ish Prime Ministers have been Peers and Peers can still have cabinet posts.
Also the formal posts within the government are in the gift of the Prime Minister and so posts and ministries have shifted somewhat over time, for example the recent separation between the Justice Ministry and Home Office.
There are also various miscellaneous but important posts such as Attorney General and Speaker of the House of Commons which aren't formally part of the government but have an important constitutional role .
That's without considering the House of Lords which has no analogy in US politics.
He has said he will resign as Prime Minister when a new leader of the Conservative party os elected.
He will still be a MP (a Member of Parliament) and retains his seat in parliament.
He could be a cabinet member under future Prime Ministers as has happened in the past. e.g. Neville Chamberlain. (and in 2024 he did become a cabinet member - Foreign Secretary)
He can remain an MP if elected as did some predecessors e.g. Ted Heath who lost the election in 1974 and so stopped being PM and became the leader of the opposition and then lost the election as Conservative Party leader the next year year. He remained an MP until 2001.
Winston Churchill who lost the party leadership and PM in 1955 and carried on as an MP until 1964.
