Q:

What is a run on the pound?

From the news today, it mentions that Jeremy Corbyn and the Labour Party is preparing to deal with a run on the pound.
What is a run on the pound? Why is it making news headlines? 
Why does Jeremy Corbyn plan for this eventuality happening?
The article says that it's where investors sell sterling en masse, but what can the Labour Government do in that situation?

A:

A "run on the pound" occurs when financial traders believe that it is not in their interest to own "pounds", but an alternative like dollars or euros, or even gold, is a better currency to own. They will then try to sell pounds, and buy the other currencies.  In order to sell quickly they reduce the price at which they are selling pounds. As this happens we say that he value of the pound has dropped. Other investors seeing this drop in price may then try to sell off their pounds very quickly, cutting the price a lot. If everyone is trying to sell, then the value of the pound can drop rapidly against other currencies.
This has several consequences. It means that it costs more for a British company to buy things from abroad. The price of imported goods and raw materials goes up. This makes things more expensive. It makes it more costly to travel abroad. On the other hand, if you are making something in Britain and selling it abroad, it makes that thing cheaper, so it makes exporting more profitable, it also makes it cheaper for tourists to visit the UK. It would add to the costs of the government and lead to higher taxes, inflation and slower growth.
There was a run on the pound after the vote to leave the EU, there was also a run on the pound when it was forced to leave the ERM in 1992
Generally a run on the pound is a bad thing it destabilises international markets that depend on predictable prices. There is a concern that the level of government borrowing implied by the Labour party's policies would cause financial traders to sell pounds in large enough amounts to cause a run, and this would be damaging to the UK economy.
As such the shadow chancellor mentioned in a meeting that he was engaged in planning for this event, even though he said it was unlikely. The fact he mentioned this possibility surprised many journalists, as predicting a run on the pound can be a self-fulfilling prophesy.
So a run on the pound is not something that the Labour party planning to have. Instead the Labour party is planning its defensive strategy if a damaging run on the pound occurs.

A:

I'm assuming that the article you referred to is the first hit on Google under "Corbyn" and "run on the pound": Jeremy Corbyn: It's right to plan for run on pound
If so, I'm afraid you're not interpreting what the article said correctly.
It says:

Jeremy Corbyn says it is "right to look at all these scenarios" after his shadow chancellor suggested that there could be a run on the pound if Labour went into government.
  John McDonnell said Labour was doing "war-game-type scenario-planning" for events such as "a run on the pound".

Corbyn doesn't want to do a run on the pound (to be more precise, this article does not say that he wants it. Whether he wants to or not is not something I know, as I don't know how to read minds yet). 
The article says that he wants to prepare how to respond in the eventuality that a run on the pound happens (intentionally or not) as a result of Labour party forming the government.

A:

I think he's overstating expectations here. There was, immediately after Brexit, a serious run on the British Pound

The British pound fell more than 10 percent on Thursday night, reaching $1.34 per pound, after midnight Eastern time, a stunning decline for a rich country's currency in a single day. The plunge came as United Kingdom  voted to leave the European Union, a historic event that shatters 40 years of efforts to foster economic integration on the continent.

Inside Britain that wouldn't have a lot of immediate effect, but over time that causes a jump in prices. So let's say it cost £100 for three barrels of oil before. A 10% drop in the value of the Pound means you now have to spend £111 for those same three barrels. Remember, the seller has to convert that currency to something they can use, so someone is having to sell Pounds. This generally leads to inflation (where prices rise in a long-term way).
There's not much a government can do to stop a run (markets are global now). In fact, in 1992 the UK tried unsuccessfully to stop the events now known as Black Wednesday, where the Pound was being short sold by a hedge fund

The UK government attempted to prop up the depreciating pound to avoid withdrawal from the monetary system the country had joined two years earlier. John Major raised interest rates to 10 percent and authorized the spending of billions worth of foreign currency reserves to buy up the sterling being sold on the currency markets, but the measures failed to prevent the pound falling below its minimum level in the ERM.

Corbyn seems to be talking about another run based on a potential Labour Party victory in the next election

The planning scenario means a Labour victory would ultimately trigger the fall in the value of the pound, which has already fallen following the Brexit vote, and could be devastating for the UK economy.

