Prime Ministers in countries that have them are usually the leader of the largest party in the lower house of their Parliament. David Cameron doesn't have to resign immediately, because he's still the leader of the largest party.
He's resigning (or rather has announced he will resign before October) because he had certainly given the impression to his party that if 'Remain' didn't win, he'd resign. He could try and stay on, but the party might get rid of him and vote to make someone else leader (therefore forcing him to resign as Prime Minister).
So he resigns, but he was elected as a representative in the lower house. That means he won't be PM anymore, and he goes back to being a member of the lower house? Does the house pick one of its own members for the job, or does the majority party get to pick anybody at all that they want to be PM?
Do PMs that leave go back to being house members? Seems like that would be kinda weird.
> So he resigns, but he was elected as a representative in the lower house. That means he won't be PM anymore, and he goes back to being a member of the lower house?
Yes.
> Does the house pick one of its own members for the job, or does the majority party get to pick anybody at all that they want to be PM?
Officially they can pick a member of either house of parliament. In practice picking a Lord would be extremely controversial and probably lead to some rapid constitutional reform.
> Do PMs that leave go back to being house members? Seems like that would be kinda weird.
They usually won't stand in the next election, and go off and do something else - either private business or charity, or one of the less direct parts of government (the house of lords, embassies or the like - traditionally Europe was another destination but I guess no longer). In theory they could stay on and work as foreign secretary or whatever for the person who replaced them (or return to the back benches) but yeah that would be weird.
> So he resigns, but he was elected as a representative in the lower house. That means he won't be PM anymore, and he goes back to being a member of the lower house?
Yep.
> Does the house pick one of its own members for the job, or does the majority party get to pick anybody at all that they want to be PM?
In most countries (the UK included) the majority party will pick one of their MPs. Australia once had a PM die in office (Harold Holt) and have a person in the Senate picked as the replacement, so the replacement ran in the byelection for the previous PM's seat.
> Do PMs that leave go back to being house members? Seems like that would be kinda weird.
Yeah, but they've also been house members the whole time they were PM, so it's not that wierd.
He's resigning (or rather has announced he will resign before October) because he had certainly given the impression to his party that if 'Remain' didn't win, he'd resign. He could try and stay on, but the party might get rid of him and vote to make someone else leader (therefore forcing him to resign as Prime Minister).