This reached a head when at the last Labour leadership election when a membership who felt largely alienated from the people who represent them voted in an old-school Labour MP, horrifying the majority of the MPs who would now be responsible to them.
A lot of the people who voted for Corbyn would then quite like to see the selection process changed, and the righter-wing Labour MPs replaced with ones who they feel represented by.
There is then a clear conflict between representing the left-wing members of Labour, and keeping enough voters onside to actually get elected. This is made far, far worse by our election system, which basically means that the only people that count are in swing seats, and thus you need to reach out to these middle-of the road voters. The route to doing that is to hold that middle ground, and assume that the people further from the centre will continue to vote for you.
The actual best solution is actually to move to some kind of list-voting system (AV or STV) or proportional system (AMS), which would allow Labour to split into two separate parties, and people to vote for the one they actually wanted without letting in the Conservatives (the same is also true of the Conservatives and UKIP, of course).
Anyone, the current Labour meltdown is caused by the membership supporting one person, the MPs supporting anyone _but_ that person, and is made most urgent by the fact that the Chilcot report into the Iraq War coming out on Wednesday, which will almost certainly tell people that Tony Blair lied to take Britain into war. Corbyn has already said that he is entirely in favour of Tony Blair being held responsible for any war crimes he might have committed. One can only imagine how this is going to go down with the MPs on the Blairite wing of the party.
Particularly as there's now a move to impeach Tony Blair. I am looking forward to this quite a lot.
*I want to make sure I understand this, so if I'm getting the facts wrong please let me know.
Original post on Dreamwidth - there are comments there.